Solve (d^2yy)/(partialx^1y)=5x

$$( d ^ { 2 } y y ) / ( \partial x ^ { 1 } y ) = 5 x$$

Solve for d (complex solution)

$$d=-y^{-\frac{1}{2}}\sqrt{5∂}x$$

$$d=y^{-\frac{1}{2}}\sqrt{5∂}x\text{, }∂\neq 0\text{ and }x\neq 0\text{ and }y\neq 0$$

Solve for x (complex solution)

$$x=-\frac{∂^{-\frac{1}{2}}\sqrt{5y}d}{5}$$

$$x=\frac{∂^{-\frac{1}{2}}\sqrt{5y}d}{5}\text{, }y\neq 0\text{ and }d\neq 0\text{ and }∂\neq 0$$

Solve for d

$$d=\sqrt{\frac{5∂}{y}}x$$

$$d=-\sqrt{\frac{5∂}{y}}x\text{, }\left(y>0\text{ and }x\neq 0\text{ and }∂>0\right)\text{ or }\left(y<0\text{ and }x\neq 0\text{ and }∂<0\right)$$

Solve for x

$$x=\frac{\sqrt{\frac{5y}{∂}}d}{5}$$

$$x=-\frac{\sqrt{\frac{5y}{∂}}d}{5}\text{, }\left(d\neq 0\text{ and }∂<0\text{ and }y<0\right)\text{ or }\left(d\neq 0\text{ and }∂>0\text{ and }y>0\right)$$