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 Oct. 3, 2024 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/

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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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