Solve xy^prime=operatorname{yn}(y/x)

$$x y ^ { \prime } = \operatorname { yn } ( \frac { y } { x } )$$

Solve for n

$$\left\{\begin{matrix}n=0\text{, }&x\neq 0\\n\in \mathrm{R}\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$x\frac{\mathrm{d}}{\mathrm{d}x}(y)x=yny$$

Multiply x and x to get x^{2}.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)=yny$$

Multiply y and y to get y^{2}.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)=y^{2}n$$

Swap sides so that all variable terms are on the left hand side.

$$y^{2}n=x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$y^{2}n=0$$

Divide 0 by y^{2}.

$$n=0$$

Solve for x

$$x\neq 0$$

$$y=0\text{ or }n=0$$