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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Example 36 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‘₯) π’…π’š/𝒅𝒙 = A 𝒄𝒐𝒔⁑𝒙" " βˆ’ B π’”π’Šπ’β‘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 π’…πŸπ’š/π’…π’™πŸ + π’š = 𝟎 Hence proved (As 𝑦 = 𝐴 𝑠𝑖𝑛⁑π‘₯+𝐡 π‘π‘œπ‘ β‘π‘₯)

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.