Whakaoti i te y^prime-ay/x=x+1/x

$$y ^ { \prime } - a \frac { y } { x } = \frac { x + 1 } { x }$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{x+1}{y}\text{, }&y\neq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=-1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$x\frac{\mathrm{d}}{\mathrm{d}x}(y)-ay=x+1$$

Tangohia te x\frac{\mathrm{d}}{\mathrm{d}x}(y) mai i ngā taha e rua.

$$-ay=x+1-x\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Whakaraupapatia anō ngā kīanga tau.

$$-ay=-x\frac{\mathrm{d}}{\mathrm{d}x}(y)+x+1$$

He hanga arowhānui tō te whārite.

$$\left(-y\right)a=x+1$$

Whakawehea ngā taha e rua ki te -y.

$$\frac{\left(-y\right)a}{-y}=\frac{x+1}{-y}$$

Mā te whakawehe ki te -y ka wetekia te whakareanga ki te -y.

$$a=\frac{x+1}{-y}$$

Whakawehe x+1 ki te -y.

$$a=-\frac{x+1}{y}$$

Whakaoti mō x

$$x=-ay-1$$

$$a=0\text{ or }y\neq -\frac{1}{a}$$