First order separable differential equation

[amolv06]

Homework Statement

$$\frac{dy}{dx} + x^{2} = x$$

Homework Equations

Above.

The Attempt at a Solution

After rearranging, I am stuck at

$$\int \frac{1}{x-x^{2}} dx = \int dt$$

I can't think of any u-substitution, or any other trick for integrals I could use to solve this.

 

[Mathdope]

Recheck you're expressions. The problem you give involves x and y, while the attempt at a solution gives x and t. Please clarify.

It looks like you should have dx/dt where you currently have dy/dx no? If that's the case consider a partial fraction decomposition.

 

[amolv06]

I wrote the wrong variable for the last integral. It should have been of dy rather than dt. I solved it. I forgot about partial fractions.

 

[HallsofIvy]

Even so, $dy/dx= x- x^2$ becomes $dy= (x- x^2)dx$. There is no need for partial fractions.

 

[fermio]

What need to find if y, then
$$y=\int(x-x^2)dx=\frac{x^2}{2}-\frac{x^3}{3}+C$$