# 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 above differential equation that satisfies the condition u=4 at t=0.

u=?

1. 👍
2. 👎
3. 👁
1. -du/u^2 = (t^3 - t) dt --->

1/u = 1/4 t^4 - 1/2 t^2 + c ---->

u = 1/[1/4 t^4 - 1/2 t^2 + c]

u=4 at t=0 ---> c = 1/4

1. 👍
2. 👎
2. du/u^2 = -(t^3 -t ) dt
1/u = (1/4)t^4 - (1/2)t^2 + constant
1/u = -t^2 (.5 -.25 t^2) + constant
u = -1/[t^2(.5 - .25 t^2) + C]

4 = -1/C so C = -4

u = -1/[t^2(.5 - .25 t^2) - 4]

1. 👍
2. 👎
3. I forgot a - sign - use his :)

1. 👍
2. 👎
4. Thanks so much. I've been struggling with that thing for days!

1. 👍
2. 👎
5. Oh - actually we agree exactly

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### 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

3. ### 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

4. ### 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 Eulerβs Method is used given βx = 0.5?

1. ### 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

2. ### 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.

3. ### 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

4. ### 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

1. ### 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

2. ### 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= ______

3. ### calc

Which of the following is the general solution of the differential equation dy dx equals the quotient of 8 times x and y?

4. ### Calculus

Suppose that we use Euler's method to approximate the solution to the differential equation ππ¦/ππ₯=π₯^4/π¦ π¦(0.1)=1 Let π(π₯,π¦)=π₯^4/π¦. We let π₯0=0.1 and π¦0=1 and pick a step size β=0.2.