# How to integrate complicated differential equation

1. Jun 19, 2011

### trojansc82

1. The problem statement, all variables and given/known data

I need to integrate ∫ -y3ey2/2

2. Relevant equations

Integration by parts

3. The attempt at a solution

I have tried several times, I am unable to find the correct solution, which is:

-yey2/2 + 2ey2/2 + c

2. Jun 19, 2011

### shelovesmath

I think you can use u substitution. Let u = y^2, du = 2y. If you factor that y^3 at y^2 * y it should work. You might have to also do integration by parts afterwards.

3. Jun 19, 2011

### Samuelb88

Try a u-substitution.

4. Jun 20, 2011

### hunt_mat

Here is a possibly slicker method, calculate:
$$\int ye^{ay^{2}}dy$$
This should be very straight forward, the result should be a function of a, all you do now is differentiate the result with respect to a and then set a=1/2.