Check sibling questions

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

Solve all your doubts with Teachoo Black (new monthly pack available now!)


Transcript

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€—

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.