# Ex 9.2, 9 - Chapter 9 Class 12 Differential Equations

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

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−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

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