# Solve the following differential equation

1. Feb 15, 2016

### fsujoseph

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

Solve the differential equation. -x2(dy/dx) + xy = x2y2 * sin(x)
2. Relevant equations
None.

3. The attempt at a solution
I first figured out that this was a Bernoulli's equation. I distributed the x2 to make it simpler. From there I divided everything by y2 to get y-2(dy/dx) + (x3/y) = x4sin(x)

From there I let w = 1/y dw=-1/y2 dy and then multiplied through by -1 so dw would fit in.

Now I have dw/dx - wx3 = -x4sin(x)

Then I let P(x) = x3 Mu(x) = eintegral(x^3)

This gave me Mu(x) = e1/4*x^4

My problem is that when you multiply that back into the equation and get to the point where you integrate, there is 3 terms on the right side (a triple integral is what you call it?). I am unsure of how to approach it, I must have done something wrong. The sin(x) is what is different from any Bernoulli's I have done. Thanks

2. Feb 15, 2016

### fsujoseph

Oh wow never mind it was -x^2 not x^-2