I(nu)dnu=8pinu^2/a^3kTdnu eching

$$I ( \nu ) d \nu = \frac { 8 \pi \nu ^ { 2 } } { a ^ { 3 } } k T d \nu$$

I uchun yechish

$$\left\{\begin{matrix}I=\frac{8\pi Tk\nu }{a^{3}}\text{, }&a\neq 0\\I\in \mathrm{R}\text{, }&\left(\nu =0\text{ or }d=0\right)\text{ and }a\neq 0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini a^{3} ga ko'paytirish.

$$I\nu d\nu a^{3}=8\pi \nu ^{2}kTd\nu$$

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

$$I\nu ^{2}da^{3}=8\pi \nu ^{2}kTd\nu$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$I\nu ^{2}da^{3}=8\pi \nu ^{3}kTd$$

Tenglama standart shaklda.

$$d\nu ^{2}a^{3}I=8\pi Tdk\nu ^{3}$$

Ikki tarafini \nu ^{2}da^{3} ga bo‘ling.

$$\frac{d\nu ^{2}a^{3}I}{d\nu ^{2}a^{3}}=\frac{8\pi Tdk\nu ^{3}}{d\nu ^{2}a^{3}}$$

\nu ^{2}da^{3} ga bo'lish \nu ^{2}da^{3} ga ko'paytirishni bekor qiladi.

$$I=\frac{8\pi Tdk\nu ^{3}}{d\nu ^{2}a^{3}}$$

8\pi \nu ^{3}kTd ni \nu ^{2}da^{3} ga bo'lish.

$$I=\frac{8\pi Tk\nu }{a^{3}}$$

T uchun yechish

$$\left\{\begin{matrix}T=\frac{Ia^{3}}{8\pi k\nu }\text{, }&\nu \neq 0\text{ and }k\neq 0\text{ and }a\neq 0\\T\in \mathrm{R}\text{, }&\left(d=0\text{ and }a\neq 0\right)\text{ or }\left(I=0\text{ and }k=0\text{ and }a\neq 0\right)\text{ or }\left(\nu =0\text{ and }a\neq 0\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini a^{3} ga ko'paytirish.

$$I\nu d\nu a^{3}=8\pi \nu ^{2}kTd\nu$$

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

$$I\nu ^{2}da^{3}=8\pi \nu ^{2}kTd\nu$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$I\nu ^{2}da^{3}=8\pi \nu ^{3}kTd$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$8\pi \nu ^{3}kTd=I\nu ^{2}da^{3}$$

Tenglama standart shaklda.

$$8\pi dk\nu ^{3}T=Id\nu ^{2}a^{3}$$

Ikki tarafini 8\pi \nu ^{3}kd ga bo‘ling.

$$\frac{8\pi dk\nu ^{3}T}{8\pi dk\nu ^{3}}=\frac{Id\nu ^{2}a^{3}}{8\pi dk\nu ^{3}}$$

8\pi \nu ^{3}kd ga bo'lish 8\pi \nu ^{3}kd ga ko'paytirishni bekor qiladi.

$$T=\frac{Id\nu ^{2}a^{3}}{8\pi dk\nu ^{3}}$$

I\nu ^{2}da^{3} ni 8\pi \nu ^{3}kd ga bo'lish.

$$T=\frac{Ia^{3}}{8\pi k\nu }$$