Problems with 2 homogeneous differential equations

Question

Hello friends. I do not see at the moment how to solve it. Thank you

Answer 1

For the first one you can set $u=y+x$. So, you get $$y'=(y+x)^2\longrightarrow u'-1=u^2$$ which is separable OE. For the second OE firstly write it as follows:

$$y'-\frac{x}{1-x^2}y=\frac{1}{1-x^2}$$ and now use a proper integrating factor regarding to the following formula: $$\mu(x)=\exp\left(\int\frac{x}{-1+x^2}dx\right)$$