Solve (x^2y+y)dy=0

$$( x ^ { 2 } y + y ) d y = 0$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=-i\text{ or }x=i\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}y+y by d.

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

Use the distributive property to multiply x^{2}yd+yd by y.

$$x^{2}dy^{2}+dy^{2}=0$$

Combine all terms containing d.

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

Divide 0 by x^{2}y^{2}+y^{2}.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}y+y by d.

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

Use the distributive property to multiply x^{2}yd+yd by y.

$$x^{2}dy^{2}+dy^{2}=0$$

Combine all terms containing d.

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

Divide 0 by x^{2}y^{2}+y^{2}.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-i\text{; }x=i\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\text{ or }y=0\end{matrix}\right.$$

Solve for x

$$x\in \mathrm{R}$$

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