
Ex 9.3
Ex 9.3, 2 Deleted for CBSE Board 2022 Exams
Ex 9.3, 3 Important Deleted for CBSE Board 2022 Exams
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Ex 9.3, 5 Important Deleted for CBSE Board 2022 Exams
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Ex 9.3, 7 Important Deleted for CBSE Board 2022 Exams
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Ex 9.3, 10 Important Deleted for CBSE Board 2022 Exams
Ex 9.3, 11 (MCQ) Deleted for CBSE Board 2022 Exams You are here
Ex 9.3, 12 (MCQ) Important Deleted for CBSE Board 2022 Exams
Last updated at Aug. 11, 2021 by Teachoo
Ex 9.3, 11 Which of the following differential equations has 𝑦=𝑐1𝑒^𝑥+𝑐2𝑒^(−𝑥) as the general solution ? (A) (𝑑^2 𝑦)/(𝑑𝑥^2 )+𝑦=0 (B) (𝑑^2 𝑦)/(𝑑𝑥^2 )−𝑦=0 (C) (𝑑^2 𝑦)/(𝑑𝑥^2 )+1=0 (D) (𝑑^2 𝑦)/(𝑑𝑥^2 )−𝑦=0 𝑦=𝑐1𝑒^𝑥+𝑐2𝑒^(−𝑥) ∴ Differentiating both sides w.r.t. 𝑥 𝑑𝑦/𝑑𝑥 =𝑐1𝑒^𝑥−𝑐2𝑒^(−𝑥) Again Differentiating both sides w.r.t. x (𝑑^2 𝑦)/(𝑑𝑥^2 ) =𝑐1𝑒^𝑥−𝑐2𝑒^(−𝑥) (−1) Since it has two variables, we will differentiate twice (𝑑^2 𝑦)/(𝑑𝑥^2 ) =𝑐1𝑒^𝑥+𝑐2𝑒^(−𝑥) (𝑑^2 𝑦)/(𝑑𝑥^2 )=𝑦 (𝑑^2 𝑦)/(𝑑𝑥^2 ) −𝑦=0 ∴ Option B is correct (Putting 𝑦=𝑐1𝑒^𝑥+𝑐2𝑒^(−𝑥))