3ydx-2xdy+x^2y^-1(10ydx-6xdy)=0 eching

$$3 y d x - 2 x d y + x ^ { 2 } y ^ { - 1 } ( 10 y d x - 6 x d y ) = 0$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&\left(x=0\text{ or }y=-4x^{2}\right)\text{ and }y\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

ydx ni olish uchun 3ydx va -2xdy ni birlashtirish.

$$ydx+x^{2}y^{-1}\left(10ydx-6xdy\right)=0$$

4ydx ni olish uchun 10ydx va -6xdy ni birlashtirish.

$$ydx+x^{2}y^{-1}\times 4ydx=0$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$ydx+x^{3}y^{-1}\times 4yd=0$$

Shartlarni qayta saralash.

$$4\times \frac{1}{y}dyx^{3}+dxy=0$$

Tenglamaning ikkala tarafini y ga ko'paytirish.

$$4\times 1dyx^{3}+dxyy=0$$

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

$$4\times 1dyx^{3}+dxy^{2}=0$$

4 hosil qilish uchun 4 va 1 ni ko'paytirish.

$$4dyx^{3}+dxy^{2}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4yx^{3}+xy^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(xy^{2}+4yx^{3}\right)d=0$$

0 ni 4yx^{3}+xy^{2} ga bo'lish.

$$d=0$$

d uchun yechish

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&\left(x=0\text{ or }y=-4x^{2}\right)\text{ and }y\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

ydx ni olish uchun 3ydx va -2xdy ni birlashtirish.

$$ydx+x^{2}y^{-1}\left(10ydx-6xdy\right)=0$$

4ydx ni olish uchun 10ydx va -6xdy ni birlashtirish.

$$ydx+x^{2}y^{-1}\times 4ydx=0$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$ydx+x^{3}y^{-1}\times 4yd=0$$

Shartlarni qayta saralash.

$$4\times \frac{1}{y}dyx^{3}+dxy=0$$

Tenglamaning ikkala tarafini y ga ko'paytirish.

$$4\times 1dyx^{3}+dxyy=0$$

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

$$4\times 1dyx^{3}+dxy^{2}=0$$

4 hosil qilish uchun 4 va 1 ni ko'paytirish.

$$4dyx^{3}+dxy^{2}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4yx^{3}+xy^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(xy^{2}+4yx^{3}\right)d=0$$

0 ni 4yx^{3}+xy^{2} ga bo'lish.

$$d=0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{i\sqrt{y}}{2}\text{; }x=0\text{; }x=-\frac{i\sqrt{y}}{2}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&d=0\text{ and }y\neq 0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x=\frac{\sqrt{-y}}{2}\text{; }x=-\frac{\sqrt{-y}}{2}\text{, }&y<0\\x\in \mathrm{R}\text{, }&d=0\text{ and }y\neq 0\end{matrix}\right,$$