Ex 9.2, 10 -  Verify solution y = root a2 - x2 , x + y dy/dx = 0

Ex 9.2, 10 - Chapter 9 Class 12 Differential Equations - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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 ))

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.