ax^2+by^prime=c eching

$$a x ^ { 2 } + b y ^ { \prime } = c$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan b\frac{\mathrm{d}}{\mathrm{d}x}(y) ni ayirish.

$$ax^{2}=c-b\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Shartlarni qayta saralash.

$$ax^{2}=-b\frac{\mathrm{d}}{\mathrm{d}x}(y)+c$$

Tenglama standart shaklda.

$$x^{2}a=c$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}a}{x^{2}}=\frac{c}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$a=\frac{c}{x^{2}}$$

b uchun yechish (complex solution)

$$b\in \mathrm{C}$$

$$c=ax^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan ax^{2} ni ayirish.

$$b\frac{\mathrm{d}}{\mathrm{d}x}(y)=c-ax^{2}$$

Shartlarni qayta saralash.

$$b\frac{\mathrm{d}}{\mathrm{d}x}(y)=-ax^{2}+c$$

Tenglama standart shaklda.

$$0=c-ax^{2}$$

Bu har qanday b uchun xato.

$$b\in$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan b\frac{\mathrm{d}}{\mathrm{d}x}(y) ni ayirish.

$$ax^{2}=c-b\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Shartlarni qayta saralash.

$$ax^{2}=-b\frac{\mathrm{d}}{\mathrm{d}x}(y)+c$$

Tenglama standart shaklda.

$$x^{2}a=c$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}a}{x^{2}}=\frac{c}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$a=\frac{c}{x^{2}}$$

b uchun yechish

$$b\in \mathrm{R}$$

$$c=ax^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan ax^{2} ni ayirish.

$$b\frac{\mathrm{d}}{\mathrm{d}x}(y)=c-ax^{2}$$

Shartlarni qayta saralash.

$$b\frac{\mathrm{d}}{\mathrm{d}x}(y)=-ax^{2}+c$$

Tenglama standart shaklda.

$$0=c-ax^{2}$$

Bu har qanday b uchun xato.

$$b\in$$