# Math Help - Differential Equations

1. ## Differential Equations

1. $y'(1+y'^{2})=ay''$

2. $y^{3}y''=1$

3. $xy''=y'ln\frac{y'}{x}$

2. 1 and 3 are reduced to first order by putting $t=y'.$

3. Originally Posted by sinichko
2. $y^{3}y''=1$
$\frac{d^2y}{dx^2} = \frac{1}{y^3}$ is solved by first making the substitution $\frac{d^2 y}{dx^2} = \frac{d}{dy}\left[ \frac{v^2}{2}\right]$ where $v = \frac{dy}{dx}$ and solving for v.