Помогите решить диф уравнение. xdy-ydx=0 x^2*dy+y^2dx=0

$\displaystyle x\text{d}y(x)-y(x)\text{d}x=0;$

$\displaystyle x\text{d}y(x)=y(x)\text{d}x;$

$\displaystyle x\frac{\text{d}y(x)}{\text{d}x}=y(x);$

$\displaystyle \frac{\text{d}y(x)}{\text{d}x}=\frac{y(x)}{x};$

$\displaystyle \frac{\frac{\text{d}y(x)}{\text{d}x}}{y(x)}=\frac{1}{x};$

$\displaystyle \int\frac{\frac{\text{d}y(x)}{\text{d}x}}{y(x)}\text{d}x=\int\frac{\text{d}x}{x};$

$\displaystyle \int\frac{\text{d}y(x)}{y(x)}=\log(x)+c_1;$

$\displaystyle \log\left(y(x)\right)=\log(x)+c_1;$

$\displaystyle e^{\log\left(y(x)\right)}=e^{\log(x)+c_1};$

$\displaystyle y(x)=xe^{c_1};$

$\displaystyle C=e^{c_1};$

$\displaystyle y(x)=\boxed{Cx}\phantom{.}.$

Решение второго уравнения аналогично.