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Ex 9.2, 8 - Verify y - cos y = x : (y sin y + cos y + x) y' = y - Gen and Particular Solution

Ex 9.2, 8 - Chapter 9 Class 12 Differential Equations - Part 2

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Ex 9.2, 8 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : π‘¦βˆ’cos⁑〖𝑦=π‘₯γ€— : (𝑦 sin⁑〖𝑦+cos⁑〖𝑦+π‘₯γ€— γ€— ) γ€– 𝑦〗^β€²=𝑦 π‘¦βˆ’cos⁑〖𝑦=π‘₯γ€— Differentiating both sides w.r.t. π‘₯ 𝑑/𝑑π‘₯ [π‘¦βˆ’γ€–cos 〗⁑𝑦 ]=𝑑π‘₯/𝑑π‘₯ 𝑑(𝑦)/𝑑π‘₯βˆ’π‘‘[cos 𝑦]/𝑑π‘₯=1 𝑑𝑦/𝑑π‘₯βˆ’(βˆ’sin 𝑦) 𝑑𝑦/𝑑π‘₯=1 𝑑𝑦/𝑑π‘₯+𝑠𝑖𝑛 𝑦 𝑑𝑦/𝑑π‘₯=1" " 𝑑𝑦/𝑑π‘₯ [1+sin 𝑦]=1 𝑑𝑦/𝑑π‘₯=1/(1 + sin 𝑦) Now, we have to verify (𝑦𝑠𝑖𝑛 𝑦+cos 𝑦+π‘₯) 𝑦^β€²=𝑦 Taking L.H.S (𝑦 sin⁑〖𝑦+cos⁑〖𝑦+π‘₯γ€— γ€— ) γ€– 𝑦〗^β€² =[𝑦𝑠𝑖𝑛 𝑦+cos 𝑦+π‘¦βˆ’cos⁑𝑦 ] 𝑦^β€² =[𝑦𝑠𝑖𝑛𝑦+𝑦] 𝑦^β€² =𝑦(1+𝑠𝑖𝑛𝑦) 𝑦^β€² =𝑦(1+𝑠𝑖𝑛𝑦)[1/(1 + sin⁑𝑦 )] =𝑦 = R.H.S Hence Verified

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.