Integrating y²/(y-1) in a separable differential equation

[crm07149]

Homework Statement

Solve the following equation by separating variables.

Homework Equations

x²y²y^' +1 = y

The Attempt at a Solution

I have been able to work through the problem to this point:

-1/x + C = int(y²/y-1)dy

I am not sure how to integrate the right hand expression int(y²/y-1)dy

 

[pbandjay]

Polynomial division of y²/(y-1) looks like it will work.

 

[ideasrule]

Have you tried u-substitution with u=y-1?

 

[crm07149]

What do you mean by polynomial division?

u-substitution with u = y-1 brings it to int(y^2/u)du, with both y and u variables

 

[pbandjay]

What do you mean by polynomial division?

http://en.wikipedia.org/wiki/Polynomial_long_division

The quotient and remainder polynomials will be easy to integrate.