Check sibling questions

Ex 9.2, 9 - Verify  x + y = tan-1 y : y2y' + y2 + 1 = 0 - Ex 9.2

Ex 9.2, 9 - Chapter 9 Class 12 Differential Equations - Part 2

Maths Crash Course - Live lectures + all videos + Real time Doubt solving!


Transcript

Ex 9.2, 9 In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : 𝑥+𝑦= tan﷮−1﷯﷮𝑦﷯ : 𝑦﷮2﷯ 𝑦﷮′﷯+ 𝑦﷮2﷯+1=0 𝑥+𝑦= tan﷮−1﷯﷮𝑦﷯ Differentiating Both Sides w.r.t. 𝑥 𝑑﷮𝑑𝑥﷯ 𝑥+𝑦﷯= 𝑑﷮𝑑𝑥﷯ tan﷮−1﷯﷮𝑦﷯﷯ 𝑑𝑥﷮𝑑𝑥﷯+ 𝑑𝑦﷮𝑑𝑥﷯= 1﷮1 + 𝑦﷮2﷯﷯. 𝑑𝑦﷮𝑑𝑥﷯ 1= 1﷮1 + 𝑦﷮2﷯﷯. 𝑑𝑦﷮𝑑𝑥﷯− 𝑑𝑦﷮𝑑𝑥﷯ 1= 𝑑𝑦﷮𝑑𝑥﷯ 1﷮1 + 𝑦﷮2﷯﷯−1﷯ 1= 𝑑𝑦﷮𝑑𝑥﷯ 1 − 1 − 𝑦﷮2﷯﷮1 + 𝑦﷮2﷯﷯﷯ 1= 𝑑𝑦﷮𝑑𝑥﷯ − 𝑦﷮2﷯﷮1 + 𝑦﷮2﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯=− 1 + 𝑦﷮2﷯﷮ 𝑦﷮2﷯﷯ Now, We Have to Verify 𝑦﷮2﷯ 𝑦﷮′﷯+ 𝑦﷮2﷯+1=0 Taking L.H.S 𝑦﷮2﷯ 𝑦﷮′﷯+ 𝑦﷮2﷯+1 = 𝑦﷮2﷯ − 1 + 𝑦﷮2﷯﷯﷮ 𝑦﷮2﷯﷯﷯+ 𝑦﷮2﷯+1 =− 1+ 𝑦﷮2﷯﷯+ 𝑦﷮2﷯+1 =−1− 𝑦﷮2﷯+ 𝑦﷮2﷯+1 =0 = R.H.S ∴ Hence Verified

Ask a doubt (live)
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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.