CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at August 14, 2026 by Teachoo
Transcript
Question 35 Find the general solution of the following differential equation: 𝑥 𝑑𝑦 − (𝑦 + 2𝑥2 )𝑑𝑥 = 0 Given 𝑥 𝑑𝑦 = (𝑦 + 2𝑥2 )𝑑𝑥 𝑑𝑦/𝑑𝑥=(𝑦 + 2𝑥^2)/𝑥 𝑑𝑦/𝑑𝑥=𝑦/𝑥+2𝑥 𝒅𝒚/𝒅𝒙−𝒚/𝒙=𝟐𝒙 Comparing with 𝒅𝒚/𝒅𝒙 + Py = Q ∴ P = (−1)/𝑥 and Q = 2x Find integrating factor IF IF = e^∫1▒𝑃𝑑𝑥 IF = 𝑒^∫1▒〖(−1)/𝑥 𝑑𝑥〗 IF = 𝑒^(−log𝑥 ) IF = 𝑒^log〖(𝑥)^(−1) 〗 IF = 𝑒^〖log 〗〖1/𝑥〗 IF = 𝟏/𝒙 Solution of the equation y × I.F = ∫1▒〖𝑸 × 𝑰.𝑭.𝒅𝒙+𝒄 〗 Putting values, 𝑦 ×1/𝑥 = ∫1▒〖2𝑥 ×1/𝑥 𝑑𝑥〗+𝐶 𝑦/𝑥 = ∫1▒2𝑑𝑥+𝐶 𝑦/𝑥 = 2𝑥+𝐶 𝒚 = 𝟐𝒙^𝟐+𝑪𝒙
