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

Question

Philoid · Accepted Answer

y = Ae^2x + 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, Ae^2x + Be^–2x = y (Given)

Hence the differential equation corresponding to the curves

y = Ae^2x + Be^–2x is

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

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