f^prime(x)=-b/mf(x)-g eching

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

b uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini m ga ko'paytirish.

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

\left(-\frac{b}{m}\right)f ni yagona kasrga aylantiring.

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

\frac{-bf}{m}x ni yagona kasrga aylantiring.

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

\frac{-bfx}{m}m ni yagona kasrga aylantiring.

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

Surat va maxrajdagi ikkala m ni qisqartiring.

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

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

gm ni ikki tarafga qo’shing.

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

Tenglama standart shaklda.

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

Ikki tarafini -fx ga bo‘ling.

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

-fx ga bo'lish -fx ga ko'paytirishni bekor qiladi.

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

gm ni -fx ga bo'lish.

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

f uchun yechish

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