f_{C}f=x^2f(x) eching

$$f _ { C } f = x ^ { 2 } f ( x )$$

f uchun yechish (complex solution)

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&f_{C}=x^{3}\end{matrix}\right,$$

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.

$$f_{C}f=x^{3}f$$

Ikkala tarafdan x^{3}f ni ayirish.

$$f_{C}f-x^{3}f=0$$

Shartlarni qayta saralash.

$$-fx^{3}+ff_{C}=0$$

f'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x^{3}+f_{C}\right)f=0$$

Tenglama standart shaklda.

$$\left(f_{C}-x^{3}\right)f=0$$

0 ni f_{C}-x^{3} ga bo'lish.

$$f=0$$

f_C uchun yechish (complex solution)

$$\left\{\begin{matrix}\\f_{C}=x^{3}\text{, }&\text{unconditionally}\\f_{C}\in \mathrm{C}\text{, }&f=0\end{matrix}\right,$$

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.

$$f_{C}f=x^{3}f$$

Tenglama standart shaklda.

$$ff_{C}=fx^{3}$$

Ikki tarafini f ga bo‘ling.

$$\frac{ff_{C}}{f}=\frac{fx^{3}}{f}$$

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

$$f_{C}=\frac{fx^{3}}{f}$$

x^{3}f ni f ga bo'lish.

$$f_{C}=x^{3}$$

f uchun yechish

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&f_{C}=x^{3}\end{matrix}\right,$$

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.

$$f_{C}f=x^{3}f$$

Ikkala tarafdan x^{3}f ni ayirish.

$$f_{C}f-x^{3}f=0$$

Shartlarni qayta saralash.

$$-fx^{3}+ff_{C}=0$$

f'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x^{3}+f_{C}\right)f=0$$

Tenglama standart shaklda.

$$\left(f_{C}-x^{3}\right)f=0$$

0 ni f_{C}-x^{3} ga bo'lish.

$$f=0$$

f_C uchun yechish

$$\left\{\begin{matrix}\\f_{C}=x^{3}\text{, }&\text{unconditionally}\\f_{C}\in \mathrm{R}\text{, }&f=0\end{matrix}\right,$$

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.

$$f_{C}f=x^{3}f$$

Tenglama standart shaklda.

$$ff_{C}=fx^{3}$$

Ikki tarafini f ga bo‘ling.

$$\frac{ff_{C}}{f}=\frac{fx^{3}}{f}$$

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

$$f_{C}=\frac{fx^{3}}{f}$$

x^{3}f ni f ga bo'lish.

$$f_{C}=x^{3}$$