# For Questions 1–2, use the differential equation given by dy/dx = xy/3, y > 0. 1. Complete the table of values x -1 -1 -1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2

45,796 results
1. ## calculus

The differential equation below models the temperature of a 87°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 67°C. Solve the differential equation to find an expression for

2. ## Differential Equation

What is the solution of the differential equation of (6x+1)y^2 dy/dx + 3x^2 +2y^3=0?

3. ## Differential Equation

what is the differential equation of (3x^2-2y^2)+(1-4xy)dy/dx=0

4. ## Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t0 [Hint: you need to

5. ## Calculus

Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑𝑥=𝑥^4/𝑦 𝑦(0.1)=1 Let 𝑓(𝑥,𝑦)=𝑥^4/𝑦. We let 𝑥0=0.1 and 𝑦0=1 and pick a step size ℎ=0.2. Euler's method is the the

6. ## Calc

Consider the differential equation dy/dx=-2x/y Find the particular solution y =f(x) to the given differential equation with the initial condition f(1) = -1

7. ## Calculus

Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

8. ## calculus

1.Solve the differential equation dy/dx= y^2/x^3 for y=f(x) with the condition y(1) = 1. 2.Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared. Explain why the initial value problem

9. ## Calculus

Consider the differential equation dy/dx = 2x - y. Let y = f(x) be the particular solution to the differential equation with the initial condition f(2) = 3. Does f have a relative min, relative max, or neither at x = 2? Since we're trying to find a max/min

10. ## Calculus BC

Let y = f(x) be the solution to the differential equation dy/dx=y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5?

11. ## math

Consider the differential equation dy/dx = -1 + (y^2/ x). Let y = g(x) be the particular solution to the differential equation dy/ dx = -1 + (y^2/ x) with initial condition g(4) = 2. Does g have a relative minimum, a relative maximum, or neither at ?

12. ## Calculus!!

Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)? Justify your answer.

13. ## Calculus

Using separation of variables, solve the following differential equation with initial conditions dy/dx = e^(2x+3y) and y(0) = 1. Hint: use a property of exponentials to rewrite the differential equation so it can be separated

14. ## calculus-differential equation

Consider the differential equation: (du/dt)=-u^2(t^3-t) a) Find the general solution to the above differential equation. (Write the answer in a form such that its numerator is 1 and its integration constant is C). u=? b) Find the particular solution of the

15. ## Differential equations in Calculus...plsssss help?

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0)

16. ## Calculus

Which of the following is a separable, first-order differential equation? A) dy/dx= x+y/2x B) dy/dx=x+y/x-y C) dy/dx=sinx

17. ## Help with differential eqs problem???? (Calculus)

Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the grocery store, the height

18. ## math

Can someone please help? Solve the differential equation dy/dx = 6xy with the condition y(0) = 40 Find the solution to the equation y= ______

19. ## Differential Equation

what is the differential equation of (6x+1)y^2 dy/dx + 3x^2 +2y^3=0

20. ## Calculus

Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.

21. ## I would like to understand my calc homework:/

Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the point (1,1). Then use your

22. ## Math

Consider a 92∘C cup of coffee placed in a 24∘C room. Suppose it is known that the coffee cools at a rate of 2∘C/min when it is 70∘C. Then according to Newton's law of cooling, the temperature T(t) of the coffee t minutes after being placed in the

23. ## calculus

is y = x^3 a solution to the differential equation xy'-3y=0?? how do i go about solving this??? also, is there a trick to understanding differential equations? i'm really struggling with this idea, but i'm too embarassed to ask my professor for help.

24. ## math

The population of a bacteria culture increases at the rate of 3 times the square root of the present population. A. Model the population P = P(t) of the bacteria population with a differential equation. B. Solve the differential equation that models the

25. ## calculus

consider dy/dx = 2-2y where y=f(x) is the particular solution to the differential equation where f(0)=2. 1. write an equation for the line tangent to f at x=0 2. is f concave up or down at (0,2)? 3. find f(x)

26. ## Calculus

A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate that’s inversely proportional to the product of the mass of the chemical present (in grams) and the time

27. ## CACULUS

dy/dx = (y-1)^2 cosπx There's a horizontal line with equation y=c that satisfies this differential equation. Find the value of c.

28. ## Calculus

These are all the questions I missed on my practice quizzes, however I was never given the correct answers. I was hoping someone could give me the answers to these so I'd be able to study them! (I know some of them were simple/dumb mistakes :')) 1. Which

29. ## calculus

consider the differential equation dy/dx= (y - 1)/ x squared where x not = 0 a) find the particular solution y= f(x) to the differential equation with the initial condition f(2)=0 (b)for the particular solution y = F(x) described in part (a) find lim F(x)

30. ## Calculus

For Questions 1–2, use the differential equation given by dy/dx = xy/3, y > 0. 1. Complete the table of values x -1 -1 -1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx 2. Find the particular solution y = f(x) to the given differential equation with the initial

31. ## Maths

The slope of a curve is equal to y divided by 4 more than x2 at any point (x, y) on the curve. A. Find a differential equation describing this curve. B. Solve the differential equation from part A. C. Suppose it’s known that as x goes to infinity on the

32. ## mathematics

Consider the fifferential equation dy/dx=(3-y)cosx.Let y=f(x)be the particular solution to the differential equation with the inital condition f(0)=1.

33. ## Calculus

Consider the differential equation dy/dx=xy-y. Find d^2y/dx^2 in terms of x and y. Describe the region in the xy plane in which all solutions curves to the differential equation are concave down.

34. ## Differential Equations

The velocity v of a freefalling skydiver is well modeled by the differential equation m*dv/dt=mg-kv^2 where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the driver during the

35. ## Calculus

For Questions 1–3, use the differential equation given by dx equals xy/3, y > 0. Complete the table of values x −1 −1 −1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx ? ? ? ? ? ? ? ? ? Find the particular solution y = f(x) to the given differential

36. ## math

The displacement s (in metres) of a body in a damped mechanical system, with no external forces satisfies the following differential equation: 6 3 2 2    dt ds dt d s where t represents time in seconds. If at time t = 0, s = 0 and  5 dt ds m/s,

37. ## calc

Let y = f(x) be the solution to the differential equation dy/dx = y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5

38. ## calculus

In a pristine lake with carrying capacity K and fishing allowed, the logistic differential equation for the population N(t) of fish at time t(in days) is dN/dt= rN(1-(N/K) - H. H= the fish harvested from the lake each day. If H= 3/16rK find all of the

39. ## Differential equation (urgent pls!!!)

Reduce the differential equation below to an exact equation (X - 2siny + 3)dx -(4siny - 2x + 3)dy=0. The problem here is how to solve for the integrating factor...any help pls?

40. ## AP Calculus Help Five Questions

1. Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = -2. 2. What function is a solution to the differential equation y ' - y = 0? 3. If dy/dx = cos^2(pi*y/4)

41. ## university maths

solve the following differential equation: (x^2+xy)dy=(xy-y^2)dx

42. ## AB Calculus

So I'm supposed to verify the solution of the differential equation. The solution is y=e^(-x). The differential equation is 3y' + 4y = e^(-x). What is the problem asking me to do here?

43. ## Calculus

dy/dx = 4ye^(5x) a) Separate the differential equation, then integrate both sides. b) Write the general solution as a function y(x). For the second part, I got y(x)=e^((5e^(5x))/(5)) + C but I don't understand how to separate differential equations and/or

44. ## Calculus PLSSSSS HELP DUE SOON

Assuming P≥0, suppose that a population develops according to the logistic equation dP/dt=0.03P−0.00015P^2 where tt is measured in weeks. Answer the following questions. 1. What is the carrying capacity? I tried solving the differential equation and

45. ## Calculus

Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2) I tried solving the differential equation and I get y = log(x^2/2 + C). Is this correct? Now I forgot how to find the equation. Thank you!

46. ## Calculus

I'm having trouble with part of a question in a problem set. The question reads as follows: Continuous price discounting. To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a

47. ## Maths

A differential equation question Find the general solution to the equation (dy/dx)^2 + sinxcos^2x(dy/dx) - sin^4x = 0 Thanks

48. ## Calculus

The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is the time in years. A. If

49. ## math

a bank account earns 7% annual interest compounded continuously. you deposit \$10,000 in the account, and withdraw money continuously from the account at a rate of \$1000 per year. a. write the differential equation for the balance, B, in the account after t

50. ## calculus

Sorry to post this again, but I am still unable to understand it and need help. Please help.1) Using 3(x-3)(x^2-6x+23)^2 as the answer to differentiating f(x)=(x^2-6x+23)^3/2, which I have been able to do, I need to find the general solution of the

51. ## Calculus

If y′= x(1+ y) and y > -1 , then y = The differential equation dy/dx=y/x^2 has a solution given by:

52. ## Physics

Verify that the formula u(t)=Acos(ωo*t+Φ) is a solution to the differential equation for the mass on a spring, by plugging this expression for u(t) directly into the differential equation: d^2u/dt^2+ωo^2*u=0.

53. ## Math

One model for the spread of rumors is one where it is assumed that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. Here y= y(t) is a function of

54. ## calculus

d=dmax (1-e^(-kt)) This equation is the result of integrating an ordinary differential equation. Derive that ODE and the associated initial condition.

55. ## Calculus

For Questions 1–2, use the differential equation given by dy/dx = xy/3, y > 0. 1. Complete the table of values x -1 -1 -1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx 2. Find the particular solution y = f(x) to the given differential equation with the initial

56. ## Math

The maximum number of arbitrary constants is equal to a. Number of derivatives in the differential equation b. Degree of differential equation c. Order of differential equation e. None of the above I don't understand this, but my guess it's letter A.

57. ## Calculus

Choose the appropriate table for the differential equation dy/dx=x-y a) x -2, 0, 1 y -4, 1, 2 dy/dx 2,-1,-1

58. ## Math

For the harmonic potential V(x,y) = x^2 + y^2 a) Find the total differential, dV. For this I got dV = 2x.dx + 2y.dy b) Given that -dV = F(x).dx + F(y).dy, where F(x) and F(y) is the force in the x and y direction, respectively, write a differential

59. ## calculus

hi! just needed help on an FRQ for ap calculus ab. let me know if you have any questions for me. I'm just really confused as far as what I am meant to do. If you could walk me through it that would be amazing. THANKS!! A population is modeled by a function

60. ## Calculus BC

Let y = f(x) be the solution to the differential equation dy/dx = y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5?

61. ## math

10. Sales of televisions grow at a rate proportional to the amount present (t is measured in days). (a)Set up a differential equation to model this problem. (b)Solve the differential equation if at t = 0, there are 20 televisions sold and after 3 days,

62. ## Ap Calculus

Ok, I've been doing BC review tests to prepare for the AP exam. I came across this free response problem and I have no idea how to do it, can someone please help me with this? It gives the differential equations: dP/dt = .03P(30-P) and it asks "Find the

63. ## MATH

Differential equations, initial value problem. The general equation of motion is: mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable. In this case, external force f(t)=0, so mx"+Bx'+kx=0 substitute

64. ## Chemistry/Math

Write a differential equation describing a second order reaction – a reaction in which the rate of depletion of the concentration of the reactants depends on the square of reactants’ concentration. Solve this differential equation and hence find an

65. ## Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t0 [Hint: you need to

66. ## calculus

Can you give me a good website on the topic, slope fields and differential equations? I need to match six slope fields with the correct differential equation. 1. dy/dx=x-y 2. dy/dx=1+x 3. dy/dx=cosx 4. dy/dx=2x 5. dy/dx=x+y 6. dy/dx=y(2-y)

67. ## Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution when t0 [Hint: you need to

68. ## Differentail Equations

I cant figure out how to do this type of problem! Consider the first order differential equation y′+(x/(x^2−4))y=(e^x)/(x−9) For each of the initial conditions below, determine the largest interval a

69. ## Calculus

The differential equation below models the temperature of an 87°C cup of coffee in a 19°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 69°C. Solve the differential equation to find an expression for

70. ## Calculus

solve the differential equation dy / dx = 11x^2y^2 with the condition that y(0) = 4 The solution to the equation is y =

71. ## Differential Equation

what is the differential equation of (2x+y+1)dx + (2y+x+1)dy=0

74. ## ordinary differential equation

consider the differential equation d^3x/dt^3 - 9(d^2x/dt^2)+ 27(dx/dt) -27x = c0s t +sin t + te^(3t) a) show that characteristic equation of the differential equation is (m-3)^3 =0 (b) Hence, find the general solution of the equation.

75. ## Differential Equations

in this problem we consider an equation in differential form M dx+N dy=0 (2y-2xy^2)dx+(2x-2x^2y)dy=0 give implicit general solutions to the differential equation. F(x,y)=

76. ## PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!

1) What are the equilibrium solutions to the differential equation and determine if it is stable or unstable with the initial condition y(-4)=1: 0.1(y+2)(4-y) 2) Use Euler's method with step size=0.5 and initial condition y(0)=3 to solve the equation

77. ## calculus

verify that y=c/x^2 is a general solution of the differential equation y'+(2/x) y=0-6y=0 then find a particular solution of the differential equation that satisfies the side condition y(1)=2

78. ## Math

a weight of mass m is attached to a spring and oscillates with simple harmonic motion. By Hooke's Law, the vertical displacement, y(t) satisfies the differential equation dy/dt=sqrt(k/m)*sqrt(A^2-y^2) where A(Fixed) is the maximum displacement and k is a

79. ## Math - derivative of sinusoidal (check)

a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x) however in the fourth

80. ## math numerical methods

Consider the following second order differential equation: y"-2x^(2)y+y^(3)=17cos(4x) with y(0)=4 , y'(0)=-9 If we let u=y and v=y′ then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as:

81. ## Math

I need to solve this set of differential equations {y'+(t/2)1, y(0)=1} and then find the limiting value as t approaches infinity. I'm not sure where to start. I found the answer to the differential equation to be: y(t)=e^-t^2/4[e^(r^2/4)dr

82. ## Physics

For the harmonic potential V(x,y) = x^2 + y^2 a)Find the total differential, dV. b) Show that dV is exact c) Given that -dV = Fx.dx + Fy.dy where Fx and Fy is the force in the x and y direction, respectively, write a differential equation describing the

83. ## Maths

Experiments show that the concentration of substance X in a ﬁrst order chemical reaction at future time (in seconds) t i.e. [X] is described by the following diﬀerential equation: d[X]/ dt= .001[X], ﬁnd: (a) Find an expression for the concentration

84. ## calculus

determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false a) the function f(x)=3/2 +cx^-2 is a solution of the differential equation xy'+2y=3 b) the differential

85. ## Chemical Engineering

When a manometer is subjected to a time dependent pressure differential, the level of liquid in the legs changes with time according to the equation: (L/g)*(d^2h/dt^2)+(8uL/ygr^2)*(dh/dt)+h = dp/yg where L = length of liquid in tube, h is the height

86. ## Calculus

Find the particular solution of the differential equation particular solution of the differential equation dy/dx=(x−7)e^(−2y).

87. ## calculus

Solve the differential equation dy/dx = -xe^y and determine the equation of the slope that passes by the point P(0,1) I get to: ∫ 1/e^y dy = - ∫ x dx which brings me to: -1/e^y + C = -x^2/2 + C? What do you do after? Thank you.

88. ## Math

Fnd the equation of the curve through the point (-1,2) of the differential equation dy/dx = -2xy/(x^2+1)

89. ## Calc

I have the differential equation dP/dt = 0.5(800-P) and I need to get the population equation P(t). Can someone walk me through the steps? Thanks!

90. ## Math

An explicit solution of a differential equation is: a) a simpler equation b) a real number c) a function on some domain d) an approximation e) a linear relation

91. ## Calculus with Diffrential Equations: Pleease help?

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0)

92. ## Calculus

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T + 5. a) Supposes that T(0)

93. ## Differential Equation

what is the differential equation of (2xy+1) + (x^2 + 3y^2)dy/dx=0

94. ## Math

What will be its differential equation? y^2-2xy+x^2=a^2

96. ## math

how do you find the differential equation for t(dy/dt)+9y=8t and y(1)=6?

97. ## Calculus

If y′= x(1+ y) and y > -1 , then y = The differential equation dy/dx=y/x^2 has a solution given by:

98. ## calculus

F''(x)=x^-3/2 f'(4)=1 f(0)=0 how do I solve this differential equation?

99. ## CALCULUS

Solve the differential equation: dy/dx = x (y^(1/3))

100. ## Calculus

Solve the differential equation f"(x)=x^2, f'(0)=3, f(0)=-1