Differential Equations

$x y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0$

$x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y=y^{\prime}$

$y^{\prime \prime}+\frac{\left(y^{\prime}\right)^2}{y}-\frac{y}{x}=0$

$y^{\prime \prime}+\left(y^{\prime}\right)^2+x^2 y^2=0$