Réitigh f^prime(x)=-b/mf(x)-g

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

Réitigh do b.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh an dá thaobh den chothromóid faoi m.

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

Scríobh \left(-\frac{b}{m}\right)f mar chodán aonair.

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

Scríobh \frac{-bf}{m}x mar chodán aonair.

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

Scríobh \frac{-bfx}{m}m mar chodán aonair.

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

Cealaigh m mar uimhreoir agus ainmneoir.

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

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

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

Cuir gm leis an dá thaobh.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -fx.

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

Má roinntear é faoi -fx cuirtear an iolrúchán faoi -fx ar ceal.

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

Roinn gm faoi -fx.

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

Réitigh do f.

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