xdx-(5y^4+3)dy=0 eching

$$x d x - ( 5 y ^ { 4 } + 3 ) d y = 0$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=-\sqrt{5y^{5}+3y}\text{ or }x=\sqrt{5y^{5}+3y}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}d-\left(5y^{4}+3\right)dy=0$$

5y^{4}+3 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}d-\left(5y^{4}d+3d\right)y=0$$

5y^{4}d+3d ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}d-\left(5dy^{5}+3dy\right)=0$$

5dy^{5}+3dy teskarisini topish uchun har birining teskarisini toping.

$$x^{2}d-5dy^{5}-3dy=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-5y^{5}-3y\right)d=0$$

0 ni x^{2}-5y^{5}-3y ga bo'lish.

$$d=0$$

d uchun yechish

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y\geq 0\text{ and }|x|=\sqrt{y\left(5y^{4}+3\right)}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}d-\left(5y^{4}+3\right)dy=0$$

5y^{4}+3 ga d ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}d-\left(5y^{4}d+3d\right)y=0$$

5y^{4}d+3d ga y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}d-\left(5dy^{5}+3dy\right)=0$$

5dy^{5}+3dy teskarisini topish uchun har birining teskarisini toping.

$$x^{2}d-5dy^{5}-3dy=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-5y^{5}-3y\right)d=0$$

0 ni x^{2}-5y^{5}-3y ga bo'lish.

$$d=0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}\\x=-\sqrt{y\left(5y^{4}+3\right)}\text{; }x=\sqrt{y\left(5y^{4}+3\right)}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\sqrt{y\left(5y^{4}+3\right)}\text{; }x=-\sqrt{y\left(5y^{4}+3\right)}\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right,$$