dy/dx=v+xdv/dx eching

$$\frac { d y } { d x } = v + \frac { x d v } { d x }$$

d uchun yechish

$$d\neq 0$$

$$v=0\text{ and }x\neq 0\text{ and }d\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

d qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini dx ga ko'paytirish.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=dxv+xdv$$

2dxv ni olish uchun dxv va xdv ni birlashtirish.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=2dxv$$

Ikkala tarafdan 2dxv ni ayirish.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}-2dxv=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x\frac{\mathrm{d}(y)}{\mathrm{d}x}-2xv\right)d=0$$

Tenglama standart shaklda.

$$\left(-2vx\right)d=0$$

0 ni -2xv ga bo'lish.

$$d=0$$

d qiymati 0 teng bo‘lmaydi.

$$d\in \emptyset$$

v uchun yechish

$$v=0$$

$$d\neq 0\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini dx ga ko'paytirish.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=dxv+xdv$$

2dxv ni olish uchun dxv va xdv ni birlashtirish.

$$dx\frac{\mathrm{d}(y)}{\mathrm{d}x}=2dxv$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2dxv=dx\frac{\mathrm{d}(y)}{\mathrm{d}x}$$

Tenglama standart shaklda.

$$2dxv=0$$

0 ni 2dx ga bo'lish.

$$v=0$$