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Question

Form the differential equation representing the family of curves y=ae2x+be2x where a and b are arbitrary constants.

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Solution

Given,

y=ae2x+be2x

differentiating on both sides, we get,

y=2ae2x2be2x

again, differentiating on both sides, we get,

y′′=4ae2x+4be2x

y′′=4(ae2x+be2x)

y′′=4y

y′′4y=0

is the required equation.

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