Q. 45.0( 1 Vote )

Form the differential equation of the family of curves y = Ae2x + Be–2x, where A and B are arbitrary constants.

Answer :

y = Ae2x + Be–2x

As the equating has two different arbitrary constants so, we can differentiate it twice with respect to x. So, on differentiating once with respect to x we get,

Again, differentiating it with respect to x, we get

But, Ae2x + Be–2x = y (Given)

Hence the differential equation corresponding to the curves

y = Ae2x + Be–2x is

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