Diff eq, need a simple step explained

[frozenguy]

So its not a problem, but a step in an example that I need explained. The section is solutions by substitutions and its an example of solving a homogeneous DE.

Step goes from:
$$\left(x^{2}+u^{2}x^{2}\right)dx+\left(x^{2} - ux^{2}\right)\left[udx + xdu\right]=0$$

to:
$$x^{2}\left(1 + u\right)dx + x^{3}\left(1-u\right)du=0$$

It had previously set y=ux, a few steps back.

 

[Mark44]

So its not a problem, but a step in an example that I need explained. The section is solutions by substitutions and its an example of solving a homogeneous DE.

Step goes from:
$$\left(x^{2}+u^{2}x^{2}\right)dx+\left(x^{2} - ux^{2}\right)\left[udx + xdu\right]=0$$

Just expand the expressions above, and simplify.
$$(x^2 + u^2x^2 + x^2u - u^2x^2)dx + (x^3 - ux^3)du = 0$$

to:
$$x^{2}\left(1 + u\right)dx + x^{3}\left(1-u\right)du=0$$

It had previously set y=ux, a few steps back.

 

[frozenguy]

Thank you... I don't know why I didn't see this before.. Ok I feel stupid. :/