(y-x^3)dx-2xdy=0 eching

$$( y - x ^ { 3 } ) d x - 2 x d y = 0$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=-x^{3}\text{ or }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y-x^{3} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(yd-x^{3}d\right)x-2xdy=0$$

yd-x^{3}d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$ydx-dx^{4}-2xdy=0$$

-ydx ni olish uchun ydx va -2xdy ni birlashtirish.

$$-ydx-dx^{4}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-yx-x^{4}\right)d=0$$

Tenglama standart shaklda.

$$\left(-x^{4}-xy\right)d=0$$

0 ni -yx-x^{4} ga bo'lish.

$$d=0$$

d uchun yechish

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=-x^{3}\text{ or }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

y-x^{3} ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(yd-x^{3}d\right)x-2xdy=0$$

yd-x^{3}d ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$ydx-dx^{4}-2xdy=0$$

-ydx ni olish uchun ydx va -2xdy ni birlashtirish.

$$-ydx-dx^{4}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-yx-x^{4}\right)d=0$$

Tenglama standart shaklda.

$$\left(-x^{4}-xy\right)d=0$$

0 ni -yx-x^{4} ga bo'lish.

$$d=0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=e^{\frac{\pi i}{3}}\sqrt[3]{y}\text{; }x=0\text{; }x=-\sqrt[3]{y}\text{; }x=e^{\frac{5\pi i}{3}}\sqrt[3]{y}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}\\x=-\sqrt[3]{y}\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right,$$