Solve the following differential equation

[fsujoseph]

Homework Statement

Solve the differential equation. -x²(dy/dx) + xy = x²y² * sin(x)

Homework Equations

None.

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) = e^{integral(x^3)}

This gave me Mu(x) = e^{1/4*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

 

[fsujoseph]

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