∫ 2dt/t^2=2/t+c eching

$$\int \frac { 2 d t } { t ^ { 2 } } = \frac { 2 } { t } + c$$

c uchun yechish

$$c=-\frac{4}{t}+С$$

$$t\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini t ga ko'paytirish.

$$t\int \frac{2}{t^{2}}\mathrm{d}t=2+tc$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2+tc=t\int \frac{2}{t^{2}}\mathrm{d}t$$

Ikkala tarafdan 2 ni ayirish.

$$tc=t\int \frac{2}{t^{2}}\mathrm{d}t-2$$

Tenglama standart shaklda.

$$tc=Сt-4$$

Ikki tarafini t ga bo‘ling.

$$\frac{tc}{t}=\frac{Сt-4}{t}$$

t ga bo'lish t ga ko'paytirishni bekor qiladi.

$$c=\frac{Сt-4}{t}$$

-4+Сt ni t ga bo'lish.

$$c=-\frac{4}{t}+С$$

t uchun yechish

$$t=\frac{4}{С-c}$$

$$c\neq С$$