CBSE Class 12 Sample Paper for 2020 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## If y = ae 2x + be βx , then show that (d 2 y)/(dx 2 ) β dy/dx β 2y = 0

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Question 22 If y = ae2x + beβx , then show that (π^2 π¦)/(ππ₯^2 ) β ππ¦/ππ₯ β 2y = 0 Given π¦=ππ^2π₯+ππ^(βπ₯) Now, ππ¦/ππ₯=2ππ^2π₯βππ^(βπ₯) And (π^2 π¦)/(ππ₯^2 )=4ππ^2π₯+ππ^(βπ₯) Now, We need to show (π^2 π¦)/(ππ₯^2 ) β ππ¦/ππ₯ β 2y = 0 Solving LHS (π^2 π¦)/(ππ₯^2 ) β ππ¦/ππ₯ β 2y = (4ππ^2π₯+ππ^(βπ₯)) β (2ππ^2π₯βππ^(βπ₯)) β 2(ππ^2π₯+ππ^(βπ₯)) = 4ππ^2π₯+ππ^(βπ₯) β 2ππ^2π₯+ππ^(βπ₯) β 2ππ^2π₯β2ππ^(βπ₯) = (4ππ^2π₯ "β " 2ππ^2π₯ "β " 2ππ^2π₯)+(ππ^(βπ₯) + ππ^(βπ₯) β2ππ^(βπ₯)) = 0 + 0 = 0 Hence proved