Solve xdy/dx+y=x^2y^2

$$\frac { x d y } { d x } + y = x ^ { 2 } y ^ { 2 }$$

Solve for d (complex solution)

$$d\neq 0$$

$$\left(x=-2\times \left(2y\right)^{-\frac{1}{2}}\text{ and }d\neq 0\text{ and }y\neq 0\right)\text{ or }\left(x=2\times \left(2y\right)^{-\frac{1}{2}}\text{ and }d\neq 0\text{ and }y\neq 0\right)\text{ or }\left(y=0\text{ and }x\neq 0\right)$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$xdy+dxy=x^{2}y^{2}dx$$

Combine xdy and dxy to get 2xdy.

$$2xdy=x^{2}y^{2}dx$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2xdy=x^{3}y^{2}d$$

Subtract x^{3}y^{2}d from both sides.

$$2xdy-x^{3}y^{2}d=0$$

Reorder the terms.

$$2dxy-dy^{2}x^{3}=0$$

Combine all terms containing d.

$$\left(2xy-y^{2}x^{3}\right)d=0$$

Divide 0 by 2xy-y^{2}x^{3}.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for d

$$d\neq 0$$

$$\left(y=0\text{ and }x\neq 0\right)\text{ or }\left(y=\frac{2}{x^{2}}\text{ and }x\neq 0\text{ and }d\neq 0\right)$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$xdy+dxy=x^{2}y^{2}dx$$

Combine xdy and dxy to get 2xdy.

$$2xdy=x^{2}y^{2}dx$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2xdy=x^{3}y^{2}d$$

Subtract x^{3}y^{2}d from both sides.

$$2xdy-x^{3}y^{2}d=0$$

Reorder the terms.

$$2dxy-dy^{2}x^{3}=0$$

Combine all terms containing d.

$$\left(2xy-y^{2}x^{3}\right)d=0$$

Divide 0 by 2xy-y^{2}x^{3}.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\sqrt{2}y^{-\frac{1}{2}}\text{; }x=\sqrt{2}y^{-\frac{1}{2}}\text{, }&y\neq 0\text{ and }d\neq 0\\x\neq 0\text{, }&y=0\text{ and }d\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{2}{y}}\text{; }x=-\sqrt{\frac{2}{y}}\text{, }&y>0\text{ and }d\neq 0\\x\neq 0\text{, }&y=0\text{ and }d\neq 0\end{matrix}\right.$$