Whakaoti i te f^prime(x)=-b/mf(x)-g

$$f ^ { \prime } ( x ) = - \frac { b } { m } f ( x ) - g$$

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{gm}{fx}\text{, }&x\neq 0\text{ and }f\neq 0\text{ and }m\neq 0\\b\in \mathrm{R}\text{, }&\left(x=0\text{ or }f=0\right)\text{ and }g=0\text{ and }m\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xm=\left(-\frac{b}{m}\right)fxm-gm$$

Tuhia te \left(-\frac{b}{m}\right)f hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xm=\frac{-bf}{m}xm-gm$$

Tuhia te \frac{-bf}{m}x hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xm=\frac{-bfx}{m}m-gm$$

Tuhia te \frac{-bfx}{m}m hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xm=\frac{-bfxm}{m}-gm$$

Me whakakore tahi te m i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)xm=-bfx-gm$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-bfx-gm=\frac{\mathrm{d}}{\mathrm{d}x}(f)xm$$

Me tāpiri te gm ki ngā taha e rua.

$$-bfx=\frac{\mathrm{d}}{\mathrm{d}x}(f)xm+gm$$

He hanga arowhānui tō te whārite.

$$\left(-fx\right)b=gm$$

Whakawehea ngā taha e rua ki te -fx.

$$\frac{\left(-fx\right)b}{-fx}=\frac{gm}{-fx}$$

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

$$b=\frac{gm}{-fx}$$

Whakawehe gm ki te -fx.

$$b=-\frac{gm}{fx}$$

Whakaoti mō f

$$\left\{\begin{matrix}f=-\frac{gm}{bx}\text{, }&x\neq 0\text{ and }b\neq 0\text{ and }m\neq 0\\f\in \mathrm{R}\text{, }&\left(x=0\text{ or }b=0\right)\text{ and }g=0\text{ and }m\neq 0\end{matrix}\right.$$