(y^2-1)*dx=(x-1)*y*dy eching

$$( y ^ { 2 } - 1 ) \cdot d x = ( x - 1 ) \cdot y \cdot d y$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=y^{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$\left(y^{2}-1\right)dx=\left(x-1\right)y^{2}d$$

y^{2}-1 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(y^{2}d-d\right)x=\left(x-1\right)y^{2}d$$

y^{2}d-d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(x-1\right)y^{2}d$$

x-1 ga y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

xy^{2}-y^{2} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=xy^{2}d-y^{2}d$$

Ikkala tarafdan xy^{2}d ni ayirish.

$$y^{2}dx-dx-xy^{2}d=-y^{2}d$$

0 ni olish uchun y^{2}dx va -xy^{2}d ni birlashtirish.

$$-dx=-y^{2}d$$

y^{2}d ni ikki tarafga qo’shing.

$$-dx+y^{2}d=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x+y^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(y^{2}-x\right)d=0$$

0 ni -x+y^{2} ga bo'lish.

$$d=0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=y^{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$\left(y^{2}-1\right)dx=\left(x-1\right)y^{2}d$$

y^{2}-1 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(y^{2}d-d\right)x=\left(x-1\right)y^{2}d$$

y^{2}d-d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(x-1\right)y^{2}d$$

x-1 ga y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

xy^{2}-y^{2} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=xy^{2}d-y^{2}d$$

Ikkala tarafdan xy^{2}d ni ayirish.

$$y^{2}dx-dx-xy^{2}d=-y^{2}d$$

0 ni olish uchun y^{2}dx va -xy^{2}d ni birlashtirish.

$$-dx=-y^{2}d$$

-1ni ikki tarafidan bekor qilish.

$$dx=y^{2}d$$

Tenglama standart shaklda.

$$dx=dy^{2}$$

Ikki tarafini d ga bo‘ling.

$$\frac{dx}{d}=\frac{dy^{2}}{d}$$

d ga bo'lish d ga ko'paytirishni bekor qiladi.

$$x=\frac{dy^{2}}{d}$$

y^{2}d ni d ga bo'lish.

$$x=y^{2}$$

d uchun yechish

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=y^{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$\left(y^{2}-1\right)dx=\left(x-1\right)y^{2}d$$

y^{2}-1 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(y^{2}d-d\right)x=\left(x-1\right)y^{2}d$$

y^{2}d-d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(x-1\right)y^{2}d$$

x-1 ga y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

xy^{2}-y^{2} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=xy^{2}d-y^{2}d$$

Ikkala tarafdan xy^{2}d ni ayirish.

$$y^{2}dx-dx-xy^{2}d=-y^{2}d$$

0 ni olish uchun y^{2}dx va -xy^{2}d ni birlashtirish.

$$-dx=-y^{2}d$$

y^{2}d ni ikki tarafga qo’shing.

$$-dx+y^{2}d=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x+y^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(y^{2}-x\right)d=0$$

0 ni -x+y^{2} ga bo'lish.

$$d=0$$

x uchun yechish

$$\left\{\begin{matrix}\\x=y^{2}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$\left(y^{2}-1\right)dx=\left(x-1\right)y^{2}d$$

y^{2}-1 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(y^{2}d-d\right)x=\left(x-1\right)y^{2}d$$

y^{2}d-d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(x-1\right)y^{2}d$$

x-1 ga y^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=\left(xy^{2}-y^{2}\right)d$$

xy^{2}-y^{2} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y^{2}dx-dx=xy^{2}d-y^{2}d$$

Ikkala tarafdan xy^{2}d ni ayirish.

$$y^{2}dx-dx-xy^{2}d=-y^{2}d$$

0 ni olish uchun y^{2}dx va -xy^{2}d ni birlashtirish.

$$-dx=-y^{2}d$$

-1ni ikki tarafidan bekor qilish.

$$dx=y^{2}d$$

Tenglama standart shaklda.

$$dx=dy^{2}$$

Ikki tarafini d ga bo‘ling.

$$\frac{dx}{d}=\frac{dy^{2}}{d}$$

d ga bo'lish d ga ko'paytirishni bekor qiladi.

$$x=\frac{dy^{2}}{d}$$

y^{2}d ni d ga bo'lish.

$$x=y^{2}$$