CBSE Class 12 Sample Paper for 2021 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 35 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

Find the general solution of the following differential equation: 𝑥 𝑑𝑦 − (𝑦 + 2𝑥 2 )𝑑𝑥 = 0

 

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

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^(−log⁡𝑥 ) 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.