1/Lv_{L}dt=di eching

$$\frac { 1 } { L } v _ { L } d t = d i$$

L uchun yechish

$$\left\{\begin{matrix}L=-itv_{L}\text{, }&t\neq 0\text{ and }v_{L}\neq 0\\L\neq 0\text{, }&d=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$1v_{L}dt=diL$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$diL=1v_{L}dt$$

Shartlarni qayta saralash.

$$iLd=dtv_{L}$$

Tenglama standart shaklda.

$$idL=dtv_{L}$$

Ikki tarafini id ga bo‘ling.

$$\frac{idL}{id}=\frac{dtv_{L}}{id}$$

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

$$L=\frac{dtv_{L}}{id}$$

v_{L}dt ni id ga bo'lish.

$$L=-itv_{L}$$

L qiymati 0 teng bo‘lmaydi.

$$L=-itv_{L}\text{, }L\neq 0$$

d uchun yechish

$$\left\{\begin{matrix}d=0\text{, }&L\neq 0\\d\in \mathrm{C}\text{, }&t=\frac{iL}{v_{L}}\text{ and }v_{L}\neq 0\text{ and }L\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini L ga ko'paytirish.

$$1v_{L}dt=diL$$

Ikkala tarafdan diL ni ayirish.

$$1v_{L}dt-diL=0$$

Shartlarni qayta saralash.

$$dtv_{L}-iLd=0$$

d'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(tv_{L}-iL\right)d=0$$

0 ni -iL+v_{L}t ga bo'lish.

$$d=0$$