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Find the general solution of the following differential equation: π‘₯ 𝑑𝑦 βˆ’ (𝑦 + 2π‘₯ 2 )𝑑π‘₯ = 0

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Find general solution of differential equation: xdy - (y + 2x^2)dx = 0

Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2
Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Part 3

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Question 35 Find the general solution of the following differential equation: π‘₯ 𝑑𝑦 βˆ’ (𝑦 + 2π‘₯2 )𝑑π‘₯ = 0 Given π‘₯ 𝑑𝑦 = (𝑦 + 2π‘₯2 )𝑑π‘₯ 𝑑𝑦/𝑑π‘₯=(𝑦 + 2π‘₯^2)/π‘₯ 𝑑𝑦/𝑑π‘₯=𝑦/π‘₯+2π‘₯ π’…π’š/π’…π’™βˆ’π’š/𝒙=πŸπ’™ Comparing with π’…π’š/𝒅𝒙 + Py = Q ∴ P = (βˆ’1)/π‘₯ and Q = 2x Find integrating factor IF IF = e^∫1▒𝑃𝑑π‘₯ IF = 𝑒^∫1β–’γ€–(βˆ’1)/π‘₯ 𝑑π‘₯γ€— IF = 𝑒^(βˆ’log⁑π‘₯ ) IF = 𝑒^log⁑〖(π‘₯)^(βˆ’1) γ€— IF = 𝑒^γ€–log 〗⁑〖1/π‘₯γ€— IF = 𝟏/𝒙 Solution of the equation y Γ— I.F = ∫1▒〖𝑸 Γ— 𝑰.𝑭.𝒅𝒙+𝒄 γ€— Putting values, 𝑦 Γ—1/π‘₯ = ∫1β–’γ€–2π‘₯ Γ—1/π‘₯ 𝑑π‘₯γ€—+𝐢 𝑦/π‘₯ = ∫1β–’2𝑑π‘₯+𝐢 𝑦/π‘₯ = 2π‘₯+𝐢 π’š = πŸπ’™^𝟐+π‘ͺ𝒙

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