# How would you solve this differential equation? dy/dx=1/2x+y-1

49,944 questions
1. ## 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

asked by Karen on December 8, 2014
2. ## 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!

asked by Robert on August 6, 2012
3. ## 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

asked by Nick on August 14, 2018
4. ## 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,

asked by Karl Haxell on May 17, 2011
5. ## 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.

asked by Rin on September 13, 2014
6. ## 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

asked by Jeff on February 5, 2008
7. ## 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

asked by A.J. on December 15, 2012
8. ## 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

asked by Emily on September 6, 2012
9. ## 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.

asked by thigan on May 21, 2016
10. ## 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,

asked by dougal on May 31, 2007
11. ## Calculus AB

Solve the differential equation: dy/dx= (x^2+y^2)/(2xy) I know how to solve this type of problem, but I am struggling getting all of the x's and y's on different sides of the equation. Thank you for your help.

asked by Jake on February 28, 2011
12. ## maths

how would i solve the differential equation dx/dt=-kx^2 i.e. solve for x as a function of t. I've been told to rearrange the equation to yield dx/x^2=-k dt but what can and should I do now?

asked by xX_Supaman_Xx on December 14, 2007
13. ## 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

asked by Alice on November 10, 2008
14. ## 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.

asked by Anonymous on March 10, 2016
15. ## 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

asked by William on May 7, 2018
16. ## 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.

asked by Michelle on May 1, 2014
17. ## 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

asked by Howie on May 10, 2018
18. ## 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)=

asked by Anonymous on February 15, 2016
19. ## 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

asked by Samantha on May 8, 2014
20. ## 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

asked by Alice on March 4, 2019
21. ## 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

asked by Anonymous on April 28, 2015
22. ## maths

Solve the following differential equation: (1 + x)*(dy/dx) = y where y is a funtion of X solve by the following: A)series expansion B) elemantary method please show working

asked by Rikki on November 29, 2011
23. ## maths

Solve the following differential equation: (1 + x)*(dy/dx) = y where y is a funtion of X solve by the following: A)series expansion B) elemantary method please show working

asked by ryan on November 30, 2011
24. ## mathematics

Solve the following differential equation: (1 + x)*(dy/dx) = y where y is a funtion of X solve by the following by: A)series expansion B) elemantary method please show working

asked by ryan on November 30, 2011
25. ## 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= ______

asked by mark on May 19, 2013
26. ## Help! Calculus

I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there. Question: Solve the differential equation. The initial condition is y(0) = 1. ((x^2+1)^(1/2))(dy/dx) -

asked by Lucy on February 1, 2017
27. ## 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?

asked by Anonymous on March 3, 2017
28. ## 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.

asked by Anonymous on March 6, 2017
29. ## Calculus

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

asked by Anonymous on November 26, 2014
30. ## Calculus

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

asked by Anonymous on February 5, 2015
31. ## Calculus

How would you solve this differential equation? dy/dx=1/2x+y-1

asked by Joe Schmo on May 1, 2011
32. ## university maths

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

asked by anonymous on November 1, 2011
33. ## Maths

asked by Taldil on February 26, 2013
34. ## Maths

asked by Taldil on February 26, 2013
35. ## Calulus 2

Solve the differential equation: dy/dx = y^2 + y

asked by Heather on October 30, 2012
36. ## Engineering Maths

asked by Taldil on February 22, 2013
37. ## CALCULUS

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

asked by Anonymous on May 29, 2012
38. ## Calculus 2

Solve the differential equation: dy/dx = y^2 + y

asked by Heather on October 30, 2012
39. ## calculus

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

asked by Chynna on January 10, 2011
40. ## 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?

asked by BEN on March 4, 2016
41. ## 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

asked by Anonymous on March 14, 2011
42. ## 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.

asked by Anonymous on April 23, 2016
43. ## Calculus I'm really confused

solve the differential equation dy/dx=y^2/x^3 for y=f(x) with condition y(1)=1.

asked by Ke\$ha on May 9, 2017
44. ## maths(Differential Equation)

Solve the differential equation below (Y + y^3/3 + x^2/2)dx + 1/4(1 + y^2)xdy=0

asked by BEN on March 3, 2016
45. ## calculus

solve the following differential equation: y' + (y)tanh(x) - 2e^x = 0

asked by Christine on May 7, 2008
46. ## calculus

Solve the following differential equation: f"(x)=sinx, x(0)=0, x'(0)=1

asked by Derek on December 6, 2011
47. ## 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

asked by Beth on November 18, 2008
48. ## Mathematics

Solve the following differential equation, i.e. solve for y: dy/dx - y/x = 1/x + y + 1 I have this so far, 1. dy/dx= (y + 1 + xy + x)/x 2. x dy = (y + 1 + xy + x)dx 3. Integrate both sides... xy + c = xy + x + .5x^2y + .5x^2 + k where c and k are constants

asked by xX_Supaman_Xx on December 29, 2007
49. ## mathematics

Solve the differential equation x^2dy+ (x-3xy + 1)=0

asked by musonda c on June 27, 2014
50. ## math

f"(x)=2, f'(2)=5, f(2)=10. solve this differential equation by finding the particular solution. How do you do this?

asked by Ed on December 1, 2009
51. ## math

can someone elxplai to me how to solve this differential equation. dy/dx= (x^2+3y^2)/2xy

asked by Anonymous on June 18, 2015
52. ## Calculus 2

solve this differential equation: dy/dt=0.06y(600-y) y(0)=10 y(t)=?

asked by Maily on March 20, 2013
53. ## Calculus

Solve the following differential equation with initial conditions: y"=e^(-2t) + 10^(4t); y(0)=1, y'(0) = 0

asked by Pax on May 15, 2015
54. ## differential equation!!

How can I solve the differential equation? C = 15ð(2Dh+(3/4)D²) + ë (94.25 Dh+35.34 D^2)/(pi D^2h/4) first dC/dD? second d^2C/dD^2? first dC/dh? second d^2C/dh^2?

asked by Alicia on November 23, 2010
55. ## Engineering Maths

Pleas help solve the ffg. differential equation: dy/dx-(1+1/x)y=y^2

asked by Taldil on February 22, 2013
56. ## Calculus

Solve the differential equation dy/dx=3x^2y^2 with the condition that y(1)=4. I know that y= -1/(x^3 + c) but what do I do with the y(1)=4 part?

asked by Ann on May 18, 2014
57. ## Maths

asked by Taldil on February 26, 2013
58. ## Math/Calculus

Solve the differential equation y'=3t^2+4. Solve the initial value problem y(0)=3. Separation of variables! My work: dy/dt= 3t^2+4 dy= 3t^2+4 dt Then you integrate both sides. ∫ dy= ∫ 3t^2+4dt Question: is there a 1 in dy? ( ∫ 1dy)? If so:

asked by Sarah on April 2, 2015
59. ## 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

asked by mari on April 10, 2012
60. ## calculus

solve the differential equation by seperation of variables 3. dy/dx=e^(2x)/4y3

asked by steve on March 17, 2011
61. ## Differential Equations

Solve the seperable differential equation for U. du/dt = e^(5u+7t) - Using the following initial condition U(0) = 12

asked by Kody on August 27, 2011
62. ## differential equations

solve the differential equation by seperation of variables 5. y'=xy/2ln y

asked by cathy on March 17, 2011
63. ## calculus

y'=xy/2ln y how do you solve the differential equation by seperation of variables

asked by smiley on March 17, 2011
64. ## Calculus

Solve the differential equation: dy/dx = (3x^2) / (y+1) with initial conditions x = -1, y = 2 I have: ∫y + 1 dy = ∫3x^2 dx (y^2 / 2) + y = x^3 + C (2^2 / 2) + (2) = (-1^3) + C? 4 = -1 + C 5 = c (y^2 / 2) + y = x^3 + 5 Is this correct?

asked by Omar on May 27, 2016
65. ## calculus

solve the differential equation that satisfies the given condition: dy/dx=(ycos(x))/(6+y^2), y(0)=1

asked by Lauren on October 17, 2015
66. ## 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.

asked by Kenneth on December 1, 2008
67. ## 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

asked by Stacey on November 30, 2014
68. ## maths sir-reiny help calculus

solve the differential equation (x^2-xy+y^2)dy-xydx=0 plz show me working

asked by samuel on October 1, 2016
69. ## Calculus

Solve the differential equation, we're using u substitution: dy/dx= 4x + (4x/ sqr root (16-x^2)) Thanks. Please respond!

asked by Taylor on December 6, 2009
70. ## maths

solve the initial value problem of the differential equation (y+sqrt(x^2+y^2))dx-xdy=0,y(3)=4

asked by Anonymous on October 1, 2016
71. ## Calculus

Solve the differential equation dy/dx = √[(x^3)(y)] with initial conditions x = 1, y = 2 so far i got y = (x^5)/25 + c so do i plug in 2 = (1^5)/25 + c 2 - (1/25) = c c = 49/25 = 1.96 is this correct?

asked by Mike on May 26, 2016
72. ## calculus

solve the firs-order differential equation by separating variables y'=xy^3/√(1+x^2)

asked by jhony on April 10, 2012
73. ## 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

asked by Kelly on October 16, 2009
74. ## 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

asked by alex on April 27, 2017
75. ## Engineering Math

solve the 1st differential equation: y1+4y=cos(x) with intial condition y(pie/3)=1

asked by Thomas on June 24, 2011
76. ## Math

dydt=10−0.2y, y(0)=10. a. Solve this differential equation, I tried solving it and I keep on getting 10. I dont know how to approach this question

asked by R on November 12, 2018
77. ## Math

dydt=10−0.2y, y(0)=10. a. Solve this differential equation, I tried solving it and I keep on getting 10. I dont know how to approach this question

asked by R on November 12, 2018
78. ## Calculus

Solve the differential equation by using Laplace transforms. Find the particular solution that satisfies them of: y''+2y'+y =4e^(-t)

asked by Elyse on July 27, 2013
79. ## Calculus

Solve the separable differential equation 10x−6ysqrt(x^2+1)dy/dx=0. with the initial condition y(0)=4.

asked by Robin on November 18, 2013
80. ## calculus

solve the differential equation. assume a, b and k are non zero constants. dR/dt = kR i don't understand how to do these problems.

asked by elizabeth on December 7, 2008
81. ## Calculus

Solve the differential equation. t(dy/dt) + 2y= t^3 t>0, y(1)=0 I think I solved it properly, I'm just trying to check my final solution.

asked by Rachel on February 15, 2011
82. ## Math

Hi. please help me solve the ffg. differential equation: D^2y=3sinx-4y given y=0 and dy/dx=1 at x=pie/2 Need full solution. Tx

asked by Ash on February 27, 2013
83. ## math

how do i solve differential equation dy/dx=3/(2-x) and use graphing utility to graph 3 solutions,one which passes through the point(1,0)

asked by mrunal on January 21, 2011
84. ## Calculus

Solve the separable differential equation: dy/dt=4y^6 and find the particular solution satisfying the initial condition y(0)=-3 y(t)=?

asked by Carly on July 29, 2011
85. ## Maths

Solve the differential equation: d2y/dx2 - 2 dy/dx + y = 3sinhx The answer should be: y(x) = e^x (Ax+ B) + ( 3^8 )(2[x^2][e^x] - [e^-x] ) Can someone please show me how to work it out?

asked by Claire on November 30, 2009
86. ## calculus

Solve the differential equation below, given the initial condition f(0) = 3. Express your answer using words or symbols. y=-5x^2

asked by Courtney on November 30, 2011
87. ## Calculus

Solve the seperable differential equation 8yyŒ =x. Use the following initial condition: y(8)=4. Express x^2 in terms of y.

asked by Robin on November 15, 2013

solve the following for x. 1)e^x^2-x=e^2 x^2-x = 2 I am not sure what to do now 2) e^-5x * e^4 = e -5x + 4 = 1 x= 3/5 3) Suppose that the price p (in dollars) and the demand in x(thousands) of a commodity satisfy the demand equation 6p + x + xp =94. How

asked by Hannah on May 1, 2011
89. ## calculus

Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."

asked by Anonymous on April 29, 2015
90. ## Maths

dx/dt = (x+2) sin^2 2t, given x=0, t=0. Solve the differential equation and calculate value x when t= pie/4, giving your answer in 3 significant figures.

asked by Zee on October 2, 2016
91. ## Differential Equations

Solve the differential equation below with initial conditions. Compute the first 6 coefficient. Find the general pattern. (1-x)y"-y'+xy=0 y(0)=1, y'(0)=1

asked by Jason on July 9, 2012
92. ## calculus

I am having alot of trouble remembering how to do this and this is a practice question for my final if you could help that would be great. Solve the differential equation (dy/dx)=(3x)/(1-x^2)

asked by Annie on May 10, 2009
93. ## 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)

asked by sammy on May 19, 2008
94. ## 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

asked by Claire on May 22, 2011
95. ## 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

asked by Mary on April 27, 2019
96. ## 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:

asked by mahdi on April 21, 2013
97. ## 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?

asked by Hannah on February 27, 2012
98. ## 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

asked by Jessica on April 25, 2007
99. ## AP Calc BC

Solve the differential equation y'= radical(x)/(-3y) i made y' dy/dx and moved the y's to one side and the x's to the other, and ended up with y^2=(-4/9)x^3/2 + c, but i'm not sure if that's write, and is that the form i'm supposed to leave it in?

asked by Anon on December 15, 2014
100. ## 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

asked by Beth on November 14, 2008