Find differential equation of the family of curves y = Aex + Be-x, wh

1.	Find differential equation of the family of curves y = Aex + Be-x, where A and B are arbitrary constant.
Answer» Given Curve is y = A.e^x+ B.e^-x ...(1) Differentiating both sides w.r.t. 'x', we have dy/dx = Ae^x - Ae^-x ...(2) Again differentiating, w.r.t. x d²y/dx² = Ae^x + Be^-x i.e., d²y/dx² = y So, (d²y/dx²) - y = 0 which is require differential Equation.

Find differential equation of the family of curves y = Aex + Be-x, where A and B are arbitrary constant.

Answer»

Given Curve is y = A.e^x+ B.e^-x ...(1)

Differentiating both sides w.r.t. 'x', we have

dy/dx = Ae^x - Ae^-x ...(2)

Again differentiating, w.r.t. x

d²y/dx² = Ae^x + Be^-x

i.e., d²y/dx² = y

So, (d²y/dx²) - y = 0

which is require differential Equation.