Ex 9.5, 3 - Find general solution: dy/dx + y/x = x2 - Ex 9.5 - Ex 9.5

part 2 - Ex 9.5, 3 - Ex 9.5 - Serial order wise - Chapter 9 Class 12 Differential Equations

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Ex 9.5, 3 For each of the differential equation given in Exercises 1 to 12, find the general solution : 𝑑𝑦/𝑑π‘₯+𝑦/π‘₯=π‘₯^2 𝑑𝑦/𝑑π‘₯+𝑦/π‘₯=π‘₯^2 Differential equation is of the form 𝑑𝑦/𝑑π‘₯+𝑃𝑦=𝑄 where P = 𝟏/𝒙 and Q = x2 Finding integrating factor, I.F = e^∫1▒〖𝑝 𝑑π‘₯γ€— IF = e^∫1β–’γ€–1/π‘₯ 𝑑π‘₯γ€— IF = e^log⁑π‘₯ IF = x Solution is y (IF) = ∫1β–’γ€–(𝑄×𝐼𝐹)𝑑π‘₯+𝑐〗 yx = ∫1▒〖𝒙^πŸΓ—π’™Γ—π’…π’™+𝒄〗 yx = ∫1β–’γ€–π‘₯^3 𝑑π‘₯+𝑐〗 yx = π‘₯^4/4+𝑐 xy = 𝒙^πŸ’/πŸ’+𝒄

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