Differential equation (cannot separate)

[Name15]

Homework Statement

Solve for y using the substitution: z = 1/(y^5)
dy/dx + y/x = (y^6)(x^3)

Homework Equations

(dz/dx) = (dz/dy) x (dy/dx)

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.

 

[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?

 

[Name15]

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

 

[Mark44]

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

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.