Differential equation (cannot separate)

1. Mar 26, 2015

Name15

1. The problem statement, all variables and given/known data
Solve for y using the substitution: z = 1/(y^5)
dy/dx + y/x = (y^6)(x^3)

2. Relevant equations
(dz/dx) = (dz/dy) x (dy/dx)

3. The attempt at a solution

I formed an equation for dz/dx but cannot separate the variables in order to integrate. Can someone tell me where I've gone wrong please.

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• ATTEMPT diff. eq..jpg
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2. Mar 26, 2015

BiGyElLoWhAt

If you rearrange your second to last step you have z' + P(x)z = Q(x).
Is all you've done in class is separable diff eq.'s?

3. Mar 26, 2015

Name15

oh, I am unfamiliar with this format. Would you mind nudging me in the right direction please?

4. Mar 26, 2015

Staff: Mentor

Find an integrating factor that you can use to multiply both sides of the equation. After multiplication, the left side of the equation should look like the product rule has been used on some function.

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