# Solve the differential equation

1. Nov 22, 2009

1. The problem statement, all variables and given/known data
a.Find solution to the differential equation
dy/dx=cos(x^2)*exp(sin(x));y(0)=0 for x in the interval [0,10]
b.find y(10)

2. Relevant equations

3. The attempt at a solution
I don't know where to begin

2. Nov 22, 2009

### Feldoh

That differential equation is separable.

3. Nov 22, 2009

I got:
y = cos(x^2)*exp(sin(x))
integral(y) = integral(cos(x^2)*exp(sin(x)))
I got stuck. What do I need to do next

4. Nov 22, 2009

### Staff: Mentor

After separation you should have
$$\int dy~=~\int cos(x^2)e^{sin(x)}dx$$

Now is a good time to verify that you have given us the correct differential equation.

5. Nov 22, 2009

I actually use ODE45 in matlab to solve the equation and plot it simultaneously.
I tried to integrate the equation using 'int' command but it did not work.
I have no clue how to solve it with only one variable on the right hand side because to solve the separable differential equation you need x and y.

6. Nov 22, 2009

### jakncoke

are u sure this is the right differential equation?

u get $$Y =~\int cos(x^2)e^{sin(x)}dx$$

but i enter the right side in mathematica and get no result

7. Nov 22, 2009

I am positive. The original equation is dy/dx = cos(x^2)*exp(sin(x))

8. Nov 22, 2009

### Staff: Mentor

For the a part,
$$y(x)~=~\int_{t = 0}^{x} cos(t^2)e^{sin(t)}dt$$

For the b part,
$$\int_{x = 0}^{10} dy~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx$$
$$\Rightarrow y(10) - y(0)~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx$$
Since y(0) = 0, then
$$y(10)~=~\int_{x = 0}^{10} cos(x^2)e^{sin(x)}dx$$

I don't think you can do much more with this if the exact solution is what is wanted.

9. Nov 22, 2009