The differential form of the equation y = ae^-2x + be^2x is: - Mathematics MCQ Mathematics Mock Test - 6 2026 | ExamTest.live

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The differential form of the equation y = a e^{- 2 x} + b e^{2 x} is:

Solution & Step-by-step Explanation

Given y = a e^{- 2 x} + b e^{2 x} .Differentiate with respect to x : y^{'} = - 2 a e^{- 2 x} + 2 b e^{2 x} Differentiate again: y^{''} = 4 a e^{- 2 x} + 4 b e^{2 x} Factor out 4: y^{''} = 4 (a e^{- 2 x} + b e^{2 x}) Since y = a e^{- 2 x} + b e^{2 x} : y^{''} = 4 y ⟹ y^{''} - 4 y = 0

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The differential form of the equation y = a e^{- 2 x} + b e^{2 x} is:

y^{''} + 4 y = 0

y^{''} - 4 y = 0

y^{''} - 2 y = 0

y^{''} + 2 y = 0

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