Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

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

Transcript

Ex 5.7, 13 If 𝑦=3 cos⁑〖 (log⁑〖π‘₯)+4 γ€– sin〗⁑〖 (log⁑〖π‘₯ )γ€— γ€— γ€— γ€—, show that π‘₯2 𝑦2 + π‘₯𝑦1 + 𝑦 = 0 𝑦=3 cos⁑〖 (log⁑〖π‘₯)+4 γ€– sin〗⁑〖 (log⁑〖π‘₯)γ€— γ€— γ€— γ€— Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑦/𝑑π‘₯ = βˆ’3 sin (log x) Γ— 1/π‘₯ + 4 cos (log x) Γ— 1/π‘₯ π‘₯ 𝑑𝑦/𝑑π‘₯ = βˆ’3 sin (log x) + 4 cos (log x) Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ (π‘₯ 𝑑𝑦/𝑑π‘₯)^β€²= (βˆ’3 sin (log x))’ + (4 cos (log x))’ (π‘₯ 𝑑𝑦/𝑑π‘₯)^β€²= βˆ’3 cos (log x) Γ— (log x)’ + 4 (βˆ’sin (log x)) Γ— (log x)’ (π‘₯ 𝑑𝑦/𝑑π‘₯)^β€²= βˆ’3 cos (log x) Γ— 1/π‘₯ βˆ’ 4 sin (log x) Γ— 1/π‘₯ π‘₯^β€² 𝑑𝑦/𝑑π‘₯ + x (𝑑𝑦/𝑑π‘₯)^β€²= βˆ’3 cos (log x) Γ— 1/π‘₯ βˆ’ 4 sin (log x) Γ— 1/π‘₯ 𝑑𝑦/𝑑π‘₯ + π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’3 cos (log x) Γ— 1/π‘₯ βˆ’ 4 sin (log x) Γ— 1/π‘₯ 𝑑𝑦/𝑑π‘₯ "+" π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (βˆ’1)/π‘₯ (3 cos (log x) + 4 sin (log x)) 𝑑𝑦/𝑑π‘₯ + π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (βˆ’1)/π‘₯ Γ— y As y = 3 cos (log x) + 4 sin (log x) π‘₯ (𝑑𝑦/𝑑π‘₯+π‘₯ (𝑑^2 𝑦)/(𝑑π‘₯^2 )) = βˆ’y π‘₯ 𝑑𝑦/𝑑π‘₯ + π‘₯^2 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = βˆ’y 𝒙^𝟐 (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) + 𝒙 π’…π’š/𝒅𝒙 + y = 0

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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.