∫ 2k/3-5y/4=-3 eching

$$\int \frac { 2 k } { 3 } - \frac { 5 y } { 4 } = - 3$$

y uchun yechish

$$y=\frac{8kx+С}{15}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 4 ga ko'paytirish.

$$4\int \frac{2k}{3}\mathrm{d}x-5y=-12$$

Ikkala tarafdan 4\int \frac{2k}{3}\mathrm{d}x ni ayirish.

$$-5y=-12-4\int \frac{2k}{3}\mathrm{d}x$$

Tenglama standart shaklda.

$$-5y=-\frac{8kx}{3}-4С-12$$

Ikki tarafini -5 ga bo‘ling.

$$\frac{-5y}{-5}=\frac{-\frac{8kx}{3}-4С-12}{-5}$$

-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.

$$y=\frac{-\frac{8kx}{3}-4С-12}{-5}$$

-12-\frac{8kx}{3}-4С ni -5 ga bo'lish.

$$y=\frac{8kx}{15}+\frac{4С}{5}+\frac{12}{5}$$

k uchun yechish

$$\left\{\begin{matrix}k=\frac{15y-С}{8x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=\frac{4С}{5}\text{ and }x=0\end{matrix}\right,$$