Whakaoti i te 3ydx-2xdy+x^2y^-1(10ydx-6xdy)=0

$$3 y d x - 2 x d y + x ^ { 2 } y ^ { - 1 } ( 10 y d x - 6 x d y ) = 0$$

Whakaoti mō d (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&\left(x=0\text{ or }y=-4x^{2}\right)\text{ and }y\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te 3ydx me -2xdy, ka ydx.

$$ydx+x^{2}y^{-1}\left(10ydx-6xdy\right)=0$$

Pahekotia te 10ydx me -6xdy, ka 4ydx.

$$ydx+x^{2}y^{-1}\times 4ydx=0$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$ydx+x^{3}y^{-1}\times 4yd=0$$

Whakaraupapatia anō ngā kīanga tau.

$$4\times \frac{1}{y}dyx^{3}+dxy=0$$

Whakareatia ngā taha e rua o te whārite ki te y.

$$4\times 1dyx^{3}+dxyy=0$$

Whakareatia te y ki te y, ka y^{2}.

$$4\times 1dyx^{3}+dxy^{2}=0$$

Whakareatia te 4 ki te 1, ka 4.

$$4dyx^{3}+dxy^{2}=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(4yx^{3}+xy^{2}\right)d=0$$

He hanga arowhānui tō te whārite.

$$\left(xy^{2}+4yx^{3}\right)d=0$$

Whakawehe 0 ki te 4yx^{3}+xy^{2}.

$$d=0$$

Whakaoti mō d

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&\left(x=0\text{ or }y=-4x^{2}\right)\text{ and }y\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Pahekotia te 3ydx me -2xdy, ka ydx.

$$ydx+x^{2}y^{-1}\left(10ydx-6xdy\right)=0$$

Pahekotia te 10ydx me -6xdy, ka 4ydx.

$$ydx+x^{2}y^{-1}\times 4ydx=0$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

$$ydx+x^{3}y^{-1}\times 4yd=0$$

Whakaraupapatia anō ngā kīanga tau.

$$4\times \frac{1}{y}dyx^{3}+dxy=0$$

Whakareatia ngā taha e rua o te whārite ki te y.

$$4\times 1dyx^{3}+dxyy=0$$

Whakareatia te y ki te y, ka y^{2}.

$$4\times 1dyx^{3}+dxy^{2}=0$$

Whakareatia te 4 ki te 1, ka 4.

$$4dyx^{3}+dxy^{2}=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(4yx^{3}+xy^{2}\right)d=0$$

He hanga arowhānui tō te whārite.

$$\left(xy^{2}+4yx^{3}\right)d=0$$

Whakawehe 0 ki te 4yx^{3}+xy^{2}.

$$d=0$$

Whakaoti mō x (complex solution)

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

Whakaoti mō x

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