Ex 9.2, 9 - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Gen and Particular Solution
Ex 9.2, 12 (MCQ) Important
Question 11 (MCQ) Deleted for CBSE Board 2024 Exams
Question 12 (MCQ) Important Deleted for CBSE Board 2024 Exams
Example 2
Ex 9.2, 1
Ex 9.2, 2
Ex 9.2, 5
Ex 9.2, 3
Example 3 Important
Ex 9.2, 7
Ex 9.2, 10
Ex 9.2, 4 Important
Ex 9.2, 8 Important
Ex 9.2, 9 You are here
Ex 9.2, 6 Important
Example 19
Misc 2 (i)
Gen and Particular Solution
Last updated at April 16, 2024 by Teachoo
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−1𝑦 : 𝑦2 𝑦′+ 𝑦2+1=0 𝑥+𝑦= tan−1𝑦 Differentiating Both Sides w.r.t. 𝑥 𝑑𝑑𝑥 𝑥+𝑦= 𝑑𝑑𝑥 tan−1𝑦 𝑑𝑥𝑑𝑥+ 𝑑𝑦𝑑𝑥= 11 + 𝑦2. 𝑑𝑦𝑑𝑥 1= 11 + 𝑦2. 𝑑𝑦𝑑𝑥− 𝑑𝑦𝑑𝑥 1= 𝑑𝑦𝑑𝑥 11 + 𝑦2−1 1= 𝑑𝑦𝑑𝑥 1 − 1 − 𝑦21 + 𝑦2 1= 𝑑𝑦𝑑𝑥 − 𝑦21 + 𝑦2 𝑑𝑦𝑑𝑥=− 1 + 𝑦2 𝑦2 Now, We Have to Verify 𝑦2 𝑦′+ 𝑦2+1=0 Taking L.H.S 𝑦2 𝑦′+ 𝑦2+1 = 𝑦2 − 1 + 𝑦2 𝑦2+ 𝑦2+1 =− 1+ 𝑦2+ 𝑦2+1 =−1− 𝑦2+ 𝑦2+1 =0 = R.H.S ∴ Hence Verified