1. ## Integrating dy/dx

I'm getting into differential equations and I am currently watching this video while trying to solve some problems: https://www.khanacademy.org/math/dif...tial-equations

He ends up with

$\displaystyle (1-y^2)dy=x^2\cdot dx$

and says: "now we can integrate".

Why can't I simply integrate dy/dx? I'm not completely oblivious as to what is going on, but I'm just trying to get the details right.

Thanks!

2. ## Re: Integrating dy/dx

What do you mean by "simply integrate dy/dx"? And with respect to what variable? I imagine you started with $\displaystyle \frac{dy}{dx}= \frac{x^2}{1- y^2}$.

You could write this as $\displaystyle \int\frac{dy}{dx}dx= \int\frac{x^2}{1- y^2}dx$. It is, of course easy to integrate on left to get just "y". But how are you going to integrate on the right? This is NOT a partial derivatives problem so you cannot just treat "y" like a constant- it is an unknown function of x so you cannot integrate it with respect to x.

3. ## Re: Integrating dy/dx

I see. Thanks !