Question 14 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Feb. 12, 2025 by Teachoo

This question is similar to Chapter 7 Class 12 Integrals - Examples

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https://www.teachoo.com/4799/727/Find-integration-log-x-or-lnx---Integration-by-Parts/category/Examples/

[Video] What is the general solution of differential equation ey′= x? - CBSE Class 12 Sample Paper for 2025 Boards

part 2 - Question 14 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Question 14 What is the general solution of the differential equation 𝑒^(𝑦^′ )=𝑥 ? (A) 𝑦=𝑥log𝑥+𝑐 (B) 𝑦=𝑥log𝑥−𝑥+𝑐 (C) 𝑦=𝑥log𝑥+𝑥+𝑐 (D) 𝑦=𝑥+𝑐Given differential equation 𝑒^(𝑦^′ )=𝑥 Taking log both sides log(𝑒^(𝑦^′ ))=log⁡𝑥 𝑦^′ × log e=log⁡𝑥 Since log e = 1 𝑦^′=𝑙𝑜𝑔⁡𝑥 𝑑𝑦/𝑑𝑥 =𝑙𝑜𝑔⁡𝑥 𝑑𝑦/𝑑𝑥 =𝑙𝑜𝑔⁡𝑥 𝑑𝑦=𝑙𝑜𝑔⁡𝑥 𝑑𝑥 Integrating both sides ∫1▒𝑑𝑦=∫1▒〖𝑙𝑜𝑔⁡𝑥 𝑑𝑥〗 𝒚=∫1▒〖𝒍𝒐𝒈⁡𝒙 𝒅𝒙〗 Putting ∫1▒〖𝑙𝑜𝑔⁡𝑥 𝑑𝑥〗=𝑥 log⁡𝑥−𝑥+𝐶 𝒚=𝒙 𝒍𝒐𝒈⁡𝒙−𝒙+𝑪 So, the correct answer is (B)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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