Whakaoti i te (y+x^2e^-x)dx-xdy=0

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

Whakaoti mō d (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te y+x^{2}e^{-x} ki te d.

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

Whakamahia te āhuatanga tohatoha hei whakarea te yd+x^{2}e^{-x}d ki te x.

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

Pahekotia te ydx me -xdy, ka 0.

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

He hanga arowhānui tō te whārite.

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

Whakawehe 0 ki te e^{-x}x^{3}.

$$d=0$$

Whakaoti mō d

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te y+x^{2}e^{-x} ki te d.

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

Whakamahia te āhuatanga tohatoha hei whakarea te yd+x^{2}e^{-x}d ki te x.

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

Pahekotia te ydx me -xdy, ka 0.

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

He hanga arowhānui tō te whārite.

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

Whakawehe 0 ki te e^{-x}x^{3}.

$$d=0$$

Whakaoti mō x (complex solution)

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

Whakaoti mō x

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