Solve xydy=x^2dy+y^2dx

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

Solve for d

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

Steps for Solving Linear Equation

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

$$xy^{2}d=x^{2}dy+y^{2}dx$$

Subtract x^{2}dy from both sides.

$$xy^{2}d-x^{2}dy=y^{2}dx$$

Subtract y^{2}dx from both sides.

$$xy^{2}d-x^{2}dy-y^{2}dx=0$$

Combine xy^{2}d and -y^{2}dx to get 0.

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

The equation is in standard form.

$$\left(-yx^{2}\right)d=0$$

Divide 0 by -x^{2}y.

$$d=0$$

Solve for x

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