d ∫ f(x) wrt x=f(x)dx eching

$$d \int f ( x ) d x = f ( x ) d x$$

d uchun yechish (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&С=\frac{fx^{2}}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$d\int fx\mathrm{d}x=fx^{2}d$$

Ikkala tarafdan fx^{2}d ni ayirish.

$$d\int fx\mathrm{d}x-fx^{2}d=0$$

Shartlarni qayta saralash.

$$d\int fx\mathrm{d}x-dfx^{2}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(\int fx\mathrm{d}x-fx^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(-\frac{fx^{2}}{2}+С\right)d=0$$

0 ni С-\frac{1}{2}fx^{2} ga bo'lish.

$$d=0$$

d uchun yechish

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&С=\frac{fx^{2}}{2}\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$d\int fx\mathrm{d}x=fx^{2}d$$

Ikkala tarafdan fx^{2}d ni ayirish.

$$d\int fx\mathrm{d}x-fx^{2}d=0$$

Shartlarni qayta saralash.

$$d\int fx\mathrm{d}x-dfx^{2}=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(\int fx\mathrm{d}x-fx^{2}\right)d=0$$

Tenglama standart shaklda.

$$\left(-\frac{fx^{2}}{2}+С\right)d=0$$

0 ni С-\frac{1}{2}fx^{2} ga bo'lish.

$$d=0$$

f uchun yechish (complex solution)

$$f\in \mathrm{C}$$

$$С=0\text{ or }d=0$$

f uchun yechish

$$f\in \mathrm{R}$$

$$С=0\text{ or }d=0$$