Ex 9.2, 10 - Chapter 9 Class 12 Differential Equations (Term 2)
Last updated at Dec. 10, 2019 by Teachoo
Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation
Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation
Ex 9.2, 10 In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : 𝑦=√(𝑎^2−𝑥^2 ) 𝑥 ∈ (−𝑎 , 𝑎) : 𝑥+𝑦 𝑑𝑦/𝑑𝑥=0(𝑦≠0)
𝑦=√(𝑎^2−𝑥^2 )
Differentiating Both Sides w.r.t 𝑥
𝑑𝑦/𝑑𝑥=(𝑑(√(𝑎^2 − 𝑥^2 )))/𝑑𝑥
=1/(2√(𝑎^2 − 𝑥^2 ))×(−2𝑥)
=(−𝑥)/√((𝑎^2 − 𝑥^2 ) )
(Using Chain Rule)
Now, We Have to Verify
𝑥+𝑦 𝑑𝑦/𝑑𝑥=0
Taking LHS
𝑥+𝑦 𝑑𝑦/𝑑𝑥 =𝑥+𝑦[(−𝑥)/√(𝑎^2 − 𝑥^2 )]
=𝑥+√(𝑎^2−𝑥^2 ) [(−𝑥)/√(𝑎^2 − 𝑥^2 )]
=𝑥−𝑥
=0
= R.H.S
Hence Verified
(█(𝑈𝑠𝑖𝑛𝑔 ) 𝑦=√(𝑎^2−𝑥^2 ))
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
