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

Please check the question here 

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

Slide36.JPG

Slide37.JPG

Go Ad-free

Transcript

Question 14 What is the general solution of the differential equation 𝑒^(𝑦^β€² )=π‘₯ ? (A) 𝑦=π‘₯logπ‘₯+𝑐 (B) 𝑦=π‘₯logπ‘₯βˆ’π‘₯+𝑐 (C) 𝑦=π‘₯logπ‘₯+π‘₯+𝑐 (D) 𝑦=π‘₯+𝑐Given differential equation 𝑒^(𝑦^β€² )=π‘₯ Taking log both sides log(𝑒^(𝑦^β€² ))=log⁑π‘₯ 𝑦^β€² Γ— log e=log⁑π‘₯ Since log e = 1 𝑦^β€²=π‘™π‘œπ‘”β‘π‘₯ 𝑑𝑦/𝑑π‘₯ =π‘™π‘œπ‘”β‘π‘₯ 𝑑𝑦/𝑑π‘₯ =π‘™π‘œπ‘”β‘π‘₯ 𝑑𝑦=π‘™π‘œπ‘”β‘π‘₯ 𝑑π‘₯ Integrating both sides ∫1▒𝑑𝑦=∫1β–’γ€–π‘™π‘œπ‘”β‘π‘₯ 𝑑π‘₯γ€— π’š=∫1β–’γ€–π’π’π’ˆβ‘π’™ 𝒅𝒙〗 Putting ∫1β–’γ€–π‘™π‘œπ‘”β‘π‘₯ 𝑑π‘₯γ€—=π‘₯ log⁑π‘₯βˆ’π‘₯+𝐢 π’š=𝒙 π’π’π’ˆβ‘π’™βˆ’π’™+π‘ͺ So, the correct answer is (B)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.