# differential equations

Most popular questions-
## Differential Equations

Suppose a small cannonball weighing 16 pounds is shot vertically upward, with an initial velocity v0 = 300 ft/s. The answer to the question "How high does the cannonball go?" depends on whether we take air resistance into account. If air resistance is

*asked by Jefferson on January 28, 2018* -
## Differential Equations

Model radioactive decay using the notation t = time (independent variable) r(t) = amount of particular radioactive isotope present at time t (dependent variable) -λ = decay rate (parameter) Note that the minus sign is used so that λ > 0 a) Using this

*asked by Quinn on January 17, 2013* -
## 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

*asked by Erica on January 24, 2013* -
## Differential Equations

Find the general solution of the given differential equation. x dy/dx − y = x^2 sin x I have solved to: y = -x cos(x) + cx The second part of the question is to give the largest interval over which the general solution is defined. I would think it would

*asked by Jefferson on February 1, 2018* -
## Differential Equations

A tank originally contains 5 lb of salt dissolved in 200 gal of water: Starting at time t=0, a salt solution containing 0.10 lb/gal is to be pumped into the tank at a constant rate and the well-stirred mixture is to flow out of the tank at the same rate.

*asked by Joe on September 17, 2012* -
## Differential equations

My homework question is to find the Laplace transform of the function f(t)=e^(10-2t)*step(t-5). I am not sure how to handle the e^(10-2t) portion of the equation. Thanks in advance.

*asked by frustrated on April 13, 2019* -
## Differential Equations

A cylindrical tank with length 5 ft and raduis of 3 ft is situated wit its axis horizontal. if a circular bottom hole with a radius of 1 in. is opened and the tank is initially half full of xylene, how long will it ake for the liquid to drain completely?

*asked by anonymous on August 31, 2010* -
## Differential Equations

Consider the spring - mass system, shown in Figure 4.2.4. consisting of two unit masses suspended from springs with spring constants 3 and 2, respectively. Assume that there is no damping in the system. Show that the displacements u1, and u2 of the masses

*asked by Daoine on May 13, 2014* -
## Differential Equations

A college professor contributes $5,000 per year into her retirement fund by making many small deposits throughout the year. The fund grows at a rate of 7% per year compounded continuously. After 30 years, she retires and begins withdrawing from her fund at

*asked by Victor on March 4, 2014* -
## 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

*asked by Erica on January 31, 2013* -
## differential equations

dS/dt = f(S) = kS(1-S/N)(S/M-1) of a fox squirrel population from the previous section. Suppose that the parameters M and k remain relatively constant over the long term but as more people move into the area. the parameter N (the carrying capacity)

*asked by Jim on February 2, 2016* -
## differential equations

Suppose the fraction of a cohort of aids patients that survives a time t after aids diagnosis is given by S(t) = exp(-kt). show that the average survival time Taver after aids diagnosis for a member of this cohort is given by Taver= 1/k. show every steps

*asked by fatih elmali on September 24, 2012* -
## Differential Equations

Hello, I am needing help to find the general solution to: dy/dt + y = te' Thanks!

*asked by Thomas on January 27, 2019* -
## differential Equations

Find general solution [t - sqrt(ty) ] dy/dt = y

*asked by George on February 14, 2018* -
## 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* -
## Differential Equations

Find the charge on the capacitor in an LRC series at t = 0.02 sec when L = 0.05 h, R = 2 Ohm, C = 0.01 farad. The initial conditions are q(0) = 5 C, i(0) = 0 Ampere. Determine the firt time at which the charge on the capacitor is equal to zero. Also, find

*asked by Chuck on April 22, 2012* -
## differential equations

the directions are to determine whether or not the equation is exact if so then solve it. the question is (x-y^3+ysinx)dx = (3xy^2+2ycosx)dy i solve and i got that it is exact because My is -3y^2+2ysinx and Nx is -3y^2+2ysinx since m and n are equal then

*asked by allison on October 8, 2008* -
## Differential equations

(X+y) dx + xdy =0

*asked by Anonymous on June 12, 2018* -
## differential Equations

laplace transform of f(t) = t sin (at) use integration by parts

*asked by George on March 29, 2018* -
## Differential Equations

Driver A had been leading archrival B for a while by a steady 3 miles. Only 2 miles from the finish, driver A ran out of gas and decelerated thereafter at a proportional to the square of his remaining speed. One mile later, driver A's speed was exactly

*asked by Won on February 26, 2013* -
## Differential Equations

a) Sketch the phase line for the differential equation dy/dt=1/((y-2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initial-value problem dy/dt=1/((y-2)(y+1))), y(0)=1/2 and compare your

*asked by Erica on February 3, 2013* -
## differential equations

Search: A 8 kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. assume that the spring constant is 40 n/ m and a damping constant is 3 N/m. At t=0 and external force of 2 sin(2t+PI/4)N is applied to the system. determine

*asked by mike on April 18, 2011* -
## Differential Equations

x dy/dx + y = 1/y^2, solve using bernoulli's equation. i got to du/dx + (2u)/x = 2x(u)^(-1/2). the u^(-1/2) is obviously a problem if im going to solve it using an integrating factor. if that is not what you yourself have gotten to then please show me my

*asked by Bryant on September 25, 2012* -
## Differential Equations

A car is traveling at 70 mph skids 240 ft after it's breaks are suddenly applied. Assuming that the cars breaking system provides a constant deceleration, find that deceleration. How long did it take the car to stop?

*asked by Jenna on June 19, 2011* -
## Differential equations

Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. So in the book I was given Newton's Heat equation. dT/dt=k(A-T) where T is

*asked by Maddie on April 13, 2018* -
## differential Equations

solve initial value problem t dy/dt = y + sqrt(t^2 + y^2) , y(1)=0

*asked by George on February 12, 2018* -
## 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* -
## Differential Equations

Use the Laplace Transform to solve this initial value problem. y'''' - 8y = 0, y'(0)=63, y''(0)=216, y'''(0)=297 I would really appreciate the help.

*asked by Emily on November 25, 2013* -
## Differential Equations

Locate the bifurcation values of a for the one-parameter family and describe the bifurcation that takes place at each such value. dy/dt=e^(-y^2)+a I got that the equilibrium points will be at -sqrt(ln(a)). I don't know if that is fine. I took the partial

*asked by Erica on February 7, 2013* -
## Differential Equations

Locate the bifurcation values of a for the one-parameter family and describe the bifurcation that takes place at each such value. dy/dt=e^(-y^2)+a I got that the equilibrium points will be at -sqrt(ln(a)). I don't know if that is fine. I took the partial

*asked by Erica on February 7, 2013* -
## differential Equations

solve the initial value problem and find the interval of existence... cos(y) dy/dt = -t sin(y)/ (1+t^2) , y(1)=pi/2

*asked by George on February 8, 2018* -
## differential equations

dS/dt = f(S) = kS(1-S/N)(S/M-1) of a fox squirrel population from the previous section. Suppose that the parameters M and k remain relatively constant over the long term but as more people move into the area. the parameter N (the carrying capacity)

*asked by Jim on February 2, 2016* -
## differential equations

Consider the 2nd order differential equation: x''(t)=-x-A(x^2-1)x'(t) x(0)= 0.5 x'0)= 0 ''= 2nd order,'= 1st order where A is a positive constant.As the value of A increases this equation becomes increasingly stiff. Convert this equation to two first-order

*asked by Rikki on November 16, 2011* -
## Differential Equations

Question 1 A particle moves on the x-axis with an acceleration , a=(6t-4)ms^-2 . Find the position and velocity of the particle at t=3 , if the particle is at origin and has a velocity of 10ms^-1 when t=0 by using either the method of undetermined

*asked by mrexp21 on November 5, 2011* -
## Differential equations

solve 1/(x^2+1) * y' + xy = 3 for y(0)=0 So I needed to find the integrating factor which is r(x)=e^(integral(p(x)dx)) so here p(x) is just x therefore r(x)=e^(x^2/2)? Then I am supposed to be able to put it in the form d/dx(r(x)y)=RHS but this doesn't

*asked by Maddie on April 13, 2018* -
## differential Equations

laplace transform of f(t) = t^2 sin (at) use integration by parts

*asked by kojo on March 29, 2018* -
## Differential Equations

We are learning how to solve systems of linear ODE's by elimination. I am not sure how to solve this: x'=-y+t y'=x-t I took the derivative of the second eqn to get y''-x'=-t' and added the two to get y''+y=-t'+t but I don't think thats the right way to

*asked by Jefferson on March 1, 2018* -
## Differential Equations

How to solve y''+y=sin(x) by separation of variables?

*asked by Jefferson on February 23, 2018* -
## Differential Equations

Find general solution. 2ty dy/dt = 3y^2 - t^2

*asked by George on February 14, 2018* -
## Differential Equations

Consider the system shown below of two masses of mass m, coupled together between two fixed walls via springs with varying spring constants. Let x(t) and y(t) be the horizontal displacements of the two masses as a function of time. (a)Write down a system

*asked by Smith on October 13, 2014* -
## differential equations

dy/dx=4x/y..verify that the straight lines y=2x are solution curves, provided x doesnt equal 0.

*asked by siddh on January 9, 2013* -
## Differential Equations

Find the general solution of the differential equation specified. 1) dy/dt= 1/(ty+1+y+1) 2) dy/dx=sec y I got y(x)=arcsin(x) for the second one. I'm not sure what to do with the first one.

*asked by Erica on January 22, 2013* -
## Differential Equations

We have a question: X'={{1,0,0} {-4,1,0} {3,6,2}}X; X(0)={-1,2,-30} I have worked out to the general solution but I don't think it's right. I have: X=C1 {0,0,1}e^2t + C2 {0,-1,6} e^t + C3 [{0,-2,6} + {0,-1,6}t] e^t this gives me x(t)=0....

*asked by Jefferson on March 20, 2018* -
## Differential Equations

Verify whether the given equation(y=c1-cos(x+c2)) is a solution to this equation[(d^2y/dx^2)^2 + (dy/dx)^2 - 1 = 0].

*asked by Alex on April 16, 2017* -
## differential equations

the general solution of the diff. eq. y' = (1/x)(y/(1-y)) - (1-x)(y/(1-y)) in implicit form is?

*asked by Anonymous on August 4, 2015* -
## Differential Equations

Solve dy/dx = y/(2y-x) using rational substitution (using v=y/x) with the initial condition y(0)=1. I solved this problem and found C (the constant) to be undefined. That is not the correct answer.

*asked by Liz on February 15, 2014* -
## 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

*asked by Erica on January 31, 2013* -
## 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

*asked by Erica on January 31, 2013* -
## Differential Equations

The boundary value problem Ty"+ ρ(ω^2)y' = 0 , y(0) = 0, y(L) = 0 is the model of the shape Of a rotating string. Suppose T and ρ are constants. Find the critical angular speed ω = ωn for which there is non-trivial solutions.

*asked by Chuck on April 22, 2012* -
## Differential Equations

Find the eigenvalues and eigenfunction for the BVP: y ' ' '+ λ2 y ' = 0 , y(0) = 0, y’(0) = 0 and y’(L) = 0

*asked by Chuck on April 22, 2012* -
## Differential Equations

A rabbit starts at the origin and runs up the right branch of the parabola y=x^2 with speed a. At the same time a dog, running with speed b, starts at the point (c,0) and pursues the rabbit. Write a differential equation for the path of the dog

*asked by Samantha on January 26, 2012* -
## differential equations

Solve the following equation explicitly by expanding up to order x5, the following 2nd order diff equation. y''(x) = (1 + x^2)*y(x) pls show working y =f(x)

*asked by zac on November 29, 2011* -
## differential equations

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

*asked by cathy on March 17, 2011* -
## Differential Equations

we are to find the power series solution for y'=xy. I have calculated to the point that I believe the answer is c_0/2^n*n! First of all is this correct and secondly, how do I write the solution in terms of c_0 * summation of something in terms of x^n?

*asked by Anonymous on April 22, 2018* -
## Differential Equations

I don't understand how to solve this. I can solve the left side and get yc, but I have no idea how to solve for the right side. y''-3y'+2y=(e^2t)/(e^t+1)

*asked by Anonymous on March 22, 2018* -
## Differential equations

Good morning. Quick question. dr/dt=K/r^2 When the radius is 3cm, the radius is increasing at a rate of 5/36pi. Use this fact to find the constant K. I know that the general form of these growth factors is e^kt but im not sure where the rate and the

*asked by Mat on February 19, 2017* -
## Differential equations

((3y^2)dx/(x^2+3x)) +( ( 2y ln ((5x)/(x+3))+ 3siny)dy=0 Please help me in solving this problem using exact differential equation. Thanks in advance.

*asked by Anonymous on September 21, 2016* -
## differential equations

rk4 method with h 0.1 solve for y' = 4x-2y, y(0)= 2; y(0.5)

*asked by Carol on August 3, 2016* -
## differential equations

Convert x''+ sin(x) = 0 into a first order system of equations. (x'' refers to the second derivative of x). I tried: y1 = sin(x) y2 = x' {y1' = cosx {y2' = -sinx Not sure if I did it right.

*asked by Sarah on November 25, 2015* -
## Differential Equations

Solve x(dy/dx)=(y^2)/(1-y log x).

*asked by Ranajoy on August 3, 2015* -
## Differential Equations

(D^2 + 1) y = 1/(1 + sin x) solve for Yp.

*asked by Cathy on October 14, 2014* -
## Differential Equations

(D^2 + 1) y = sec^2 (x) tan (x) solve for Yp.

*asked by Cathy on October 14, 2014* -
## Differential Equations

(D^2 + 1) y = sec^3 x solve for Yp.

*asked by Cathy on October 14, 2014* -
## Differential Equations

(D^2 + 1) y = sec^2 2x solve for Yp.

*asked by Cathy on October 14, 2014* -
## Differential Equations

(a) Let S be the set of solutions y(t) to the differential equation dy/dt = -y for t> 0. With addition and scalar multiplication of elements defined in the usual way, is S a vector space? (b)Let T be the set of solution y(t) to the differential equation

*asked by Cam on October 13, 2014* -
## Differential Equations

Classify the following differential equations as linear or nonlinear: 3x' +5x=7t^2 4x^2+2x+5tx=0

*asked by Connor on September 11, 2014* -
## Differential Equations

(x^2+1)dx+x^2y^2dy=0 need help:)..thanks.

*asked by Alyanna on July 14, 2014* -
## Differential Equations

y'=2x+y. Find a solution whose graph is also an isocline.

*asked by Brian on February 14, 2013* -
## Differential Equations

a) Sketch the phase line for the differential equation dy/dt=1/((y-2)(y+1)) and discuss the behavior of the solution with initial condition y(0)=1/2 b) Apply analytic techniques to the initial-value problem dy/dt=1/((y-2)(y+1))), y(0)=1/2 and compare your

*asked by Erica on February 3, 2013* -
## Differential Equations

For the following initial value problem: dy/dt=1/((y+1)(t-2)), y(0)=0 a)Find a formula for the solution. b) State the domain of definition of the solution. c) Describe what happens to the solution as it approaches the limit of its domain of definition. Why

*asked by Erica on January 31, 2013* -
## Differential Equations

For the following initial value problem: dy/dt=1/((y+1)(t-2)) a)Find a formula for the solution. b) State the domain of definition of the solution. c) Describe what happens to the solution as it approaches the limit of its domain of definition. Why can't

*asked by Erica on January 31, 2013* -
## Differential Equations

A government agency has a current staff of 5000, of whom 25% are women. Employees are quitting randomly at the rate of 100 per week. Replacements are being hired at the rate of 50 per week, with the requirement that half be women. Interested in the rate of

*asked by bryant on October 30, 2012* -
## 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* -
## Differential Equations

solve using variation of parameters: y"+36y=[csc(6t)]^2 I don't understand variation of parameters very well at all.

*asked by Rosy on April 24, 2012*