Question 11 (MCQ) - Gen and Particular Solution - Chapter 9 Class 12 Differential Equations
Last updated at April 16, 2024 by Teachoo
Gen and Particular Solution
Ex 9.2, 12 (MCQ) Important
Question 11 (MCQ) Deleted for CBSE Board 2024 Exams You are here
Question 12 (MCQ) Important Deleted for CBSE Board 2024 Exams
Example 2
Ex 9.2, 1
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Ex 9.2, 3
Example 3 Important
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Ex 9.2, 4 Important
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Ex 9.2, 6 Important
Example 19
Misc 2 (i)
Gen and Particular Solution
Last updated at April 16, 2024 by Teachoo
Question 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))