3ay^2dy=ay^3+c eching

$$3 a y ^ { 2 } d y = a y ^ { 3 } + c$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{c}{\left(3d-1\right)y^{3}}\text{, }&y\neq 0\text{ and }d\neq \frac{1}{3}\\a\in \mathrm{C}\text{, }&\left(y=0\text{ or }d=\frac{1}{3}\right)\text{ and }c=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$3ay^{3}d=ay^{3}+c$$

Ikkala tarafdan ay^{3} ni ayirish.

$$3ay^{3}d-ay^{3}=c$$

Shartlarni qayta saralash.

$$3ady^{3}-ay^{3}=c$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3dy^{3}-y^{3}\right)a=c$$

Ikki tarafini 3dy^{3}-y^{3} ga bo‘ling.

$$\frac{\left(3dy^{3}-y^{3}\right)a}{3dy^{3}-y^{3}}=\frac{c}{3dy^{3}-y^{3}}$$

3dy^{3}-y^{3} ga bo'lish 3dy^{3}-y^{3} ga ko'paytirishni bekor qiladi.

$$a=\frac{c}{3dy^{3}-y^{3}}$$

c ni 3dy^{3}-y^{3} ga bo'lish.

$$a=\frac{c}{\left(3d-1\right)y^{3}}$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{c}{\left(3d-1\right)y^{3}}\text{, }&y\neq 0\text{ and }d\neq \frac{1}{3}\\a\in \mathrm{R}\text{, }&\left(y=0\text{ or }d=\frac{1}{3}\right)\text{ and }c=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$3ay^{3}d=ay^{3}+c$$

Ikkala tarafdan ay^{3} ni ayirish.

$$3ay^{3}d-ay^{3}=c$$

Shartlarni qayta saralash.

$$3ady^{3}-ay^{3}=c$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(3dy^{3}-y^{3}\right)a=c$$

Ikki tarafini 3dy^{3}-y^{3} ga bo‘ling.

$$\frac{\left(3dy^{3}-y^{3}\right)a}{3dy^{3}-y^{3}}=\frac{c}{3dy^{3}-y^{3}}$$

3dy^{3}-y^{3} ga bo'lish 3dy^{3}-y^{3} ga ko'paytirishni bekor qiladi.

$$a=\frac{c}{3dy^{3}-y^{3}}$$

c ni 3dy^{3}-y^{3} ga bo'lish.

$$a=\frac{c}{\left(3d-1\right)y^{3}}$$

c uchun yechish

$$c=a\left(3d-1\right)y^{3}$$