Solve dx/ylny+4dy/sqrt{x}=0

$$\frac { d x } { y \ln y } + \frac { 4 d y } { \sqrt { x } } = 0$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&y\neq 1\text{ and }y>0\text{ and }x>0\\d\in \mathrm{R}\text{, }&x=\left(2y\right)^{\frac{4}{3}}\ln(y)^{\frac{2}{3}}\text{ and }y>0\text{ and }y<1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=y^{\frac{4}{3}}\times \left(4\ln(y)\right)^{\frac{2}{3}}\text{, }&y>0\text{ and }y<1\\x>0\text{, }&d=0\text{ and }y\neq 1\text{ and }y>0\end{matrix}\right.$$