y^prime-ay/x=x+1/x eching

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

a uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

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

Ikkala tarafdan x\frac{\mathrm{d}}{\mathrm{d}x}(y) ni ayirish.

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

Shartlarni qayta saralash.

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

Tenglama standart shaklda.

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

Ikki tarafini -y ga bo‘ling.

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

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

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

x+1 ni -y ga bo'lish.

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

x uchun yechish

$$x=-ay-1$$

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