Ex 9.2, 10 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Gen and Particular Solution
Gen and Particular Solution
Last updated at Dec. 16, 2024 by Teachoo
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 ))