If y=e^ 4x +2e^ -x satisfies the equation d^2y dx^2 +A dy dx +By=0, then the values of A and B are respectively

MHT CET 2022 Mathematics question

If satisfies the equation , then the values of A and B are respectively

Answer: (B)

Since is a combination of and , the auxiliary equation has roots and . So , giving the differential equation . Comparing with

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Question ID VK-094351