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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Example 39 If 𝑦 = A sin⁑π‘₯+B cos⁑π‘₯, then prove that 𝑑2𝑦/𝑑π‘₯2 + y = 0. 𝑦 = A sin⁑π‘₯+B cos⁑π‘₯ Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = 𝑑(A sin⁑π‘₯ + B cos⁑π‘₯" " )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 𝑑(A sin⁑π‘₯ )/𝑑π‘₯ + 𝑑(B cos⁑π‘₯ )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = A . 𝑑(sin⁑π‘₯ )/𝑑π‘₯ + B . 𝑑(cos⁑π‘₯" " )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = A cos⁑π‘₯" " + B (βˆ’ sin⁑π‘₯) 𝑑𝑦/𝑑π‘₯ = A cos⁑π‘₯" " βˆ’ B sin⁑π‘₯ Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ (𝑑^2 𝑦)/〖𝑑π‘₯γ€—^2 = (𝑑 (γ€–A cos〗⁑π‘₯" " " βˆ’" γ€–B sin〗⁑π‘₯ ") " )/𝑑π‘₯ (𝑑^2 𝑦)/〖𝑑π‘₯γ€—^2 = 𝑑(A cos⁑π‘₯ )/𝑑π‘₯ βˆ’ 𝑑(B sin⁑π‘₯" " )/𝑑π‘₯ (𝑑^2 𝑦)/〖𝑑π‘₯γ€—^2 = –A sin⁑π‘₯ βˆ’ B cos⁑π‘₯ (𝑑^2 𝑦)/〖𝑑π‘₯γ€—^2 = – (A sin⁑π‘₯ + B cos⁑π‘₯) (𝑑^2 𝑦)/〖𝑑π‘₯γ€—^2 = –y 𝑑2𝑦/𝑑π‘₯2 + 𝑦 = 0 Hence proved As 𝑦 = 𝐴 𝑠𝑖𝑛⁑π‘₯+𝐡 π‘π‘œπ‘ β‘π‘₯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.