Question 11 (MCQ) - Gen and Particular Solution - Chapter 9 Class 12 Differential Equations

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Ex 9.3, 11 - Which differential equations has y = c1 ex + c2 e-x

Ex 9.3, 11 - Chapter 9 Class 12 Differential Equations - Part 2

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Question 11 Which of the following differential equations has š‘¦=š‘1š‘’^š‘„+š‘2š‘’^(āˆ’š‘„) as the general solution ? (A) (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )+š‘¦=0 (B) (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )āˆ’š‘¦=0 (C) (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )+1=0 (D) (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )āˆ’š‘¦=0 š‘¦=š‘1š‘’^š‘„+š‘2š‘’^(āˆ’š‘„) āˆ“ Differentiating both sides w.r.t. š‘„ š‘‘š‘¦/š‘‘š‘„ =š‘1š‘’^š‘„āˆ’š‘2š‘’^(āˆ’š‘„) Again Differentiating both sides w.r.t. x (š‘‘^2 š‘¦)/(š‘‘š‘„^2 ) =š‘1š‘’^š‘„āˆ’š‘2š‘’^(āˆ’š‘„) (āˆ’1) Since it has two variables, we will differentiate twice (š‘‘^2 š‘¦)/(š‘‘š‘„^2 ) =š‘1š‘’^š‘„+š‘2š‘’^(āˆ’š‘„) (š‘‘^2 š‘¦)/(š‘‘š‘„^2 )=š‘¦ (š‘‘^2 š‘¦)/(š‘‘š‘„^2 ) āˆ’š‘¦=0 āˆ“ Option B is correct (Putting š‘¦=š‘1š‘’^š‘„+š‘2š‘’^(āˆ’š‘„))

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