![Slide5.JPG](https://d1avenlh0i1xmr.cloudfront.net/84366110-a77c-4a60-8340-ba27b898c197/slide5.jpg)
![Slide6.JPG](https://d1avenlh0i1xmr.cloudfront.net/01430f54-f45c-402f-9c8e-d77b7d7a9c1e/slide6.jpg)
Examples
Last updated at April 16, 2024 by Teachoo
Example 15 Find the general solution of the differential equation π₯ ππ¦/ππ₯+2π¦=π₯^2 (π₯β 0) π₯ ππ¦/ππ₯+2π¦=π₯^2 (π₯ ππ¦)/(π₯ ππ₯) + 2π¦/π₯ = π₯^2/π₯ Dividing both sides by x π π/π π + ππ/π = x Differential equation is of the form ππ¦/ππ₯+ππ¦=π where P = 2/π₯ & Q = x Finding Integrating Factor IF = π^β«1βγπ ππ₯γ IF = π^β«1βγπ/π π πγ IF = π^(2 logβ‘π₯ ) IF = π^(γlogβ‘π₯γ^2 ) I.F = x2 Solution of differential equation is y Γ IF = β«1βγ(πΈΓππ )π π+πγ yx2 = β«1βγπ₯Γπ₯^2 ππ₯+πγ yx2 = β«1βγπ^π π π+πγ x2 y = π₯^4/4+π y = π^π/π+ππ^(βπ) is the required general solution