Ex 5.7, 11 - If y = 5 cos x - 3 sin x, prove d2y/dx2 + y = 0

Ex 5.7, 11 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Ex 5.7, 11 If y=5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€— ,prove that 𝑑2𝑦/𝑑π‘₯2 + y = 0 y = 5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€— Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€—))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(5 cos⁑π‘₯))/𝑑π‘₯ βˆ’ (𝑑(3 sin⁑π‘₯))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = βˆ’ 5 sin⁑π‘₯ βˆ’ 3 cos⁑π‘₯ Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯) = (𝑑 γ€–(βˆ’ 5 sin〗⁑π‘₯ γ€–βˆ’ 3cos〗⁑〖π‘₯)γ€—)/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’(𝑑(5 sin⁑π‘₯))/𝑑π‘₯ βˆ’ (𝑑(3 cos⁑π‘₯))/𝑑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ 5 cos⁑π‘₯ βˆ’ 3 γ€–(βˆ’sin〗⁑〖π‘₯)γ€— (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ 5 cos⁑π‘₯ + 3 sin⁑π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’ (5 cos⁑π‘₯ βˆ’ 3 sin⁑π‘₯) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’y (𝑑^2 𝑦)/(𝑑π‘₯^2 ) + y = 0 Hence Proved As y = 5 cos⁑〖π‘₯βˆ’3 sin⁑π‘₯ γ€—

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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.