Solve (y+x^2e^-x)dx-xdy=0

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

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$\left(yd+x^{2}e^{-x}d\right)x-xdy=0$$

Use the distributive property to multiply yd+x^{2}e^{-x}d by x.

$$ydx+e^{-x}dx^{3}-xdy=0$$

Combine ydx and -xdy to get 0.

$$e^{-x}dx^{3}=0$$

The equation is in standard form.

$$\frac{x^{3}}{e^{x}}d=0$$

Divide 0 by e^{-x}x^{3}.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

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

$$\left(yd+x^{2}e^{-x}d\right)x-xdy=0$$

Use the distributive property to multiply yd+x^{2}e^{-x}d by x.

$$ydx+e^{-x}dx^{3}-xdy=0$$

Combine ydx and -xdy to get 0.

$$e^{-x}dx^{3}=0$$

The equation is in standard form.

$$\frac{x^{3}}{e^{x}}d=0$$

Divide 0 by e^{-x}x^{3}.

$$d=0$$

Solve for x (complex solution)

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

Solve for x

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