Verify that the function `y=c_1e^(ax ) """"cosb x+c_2""""e^(ax)"" sinb x` , where `c_1,""""c_2` are arbitrary constants is a solution of the differential equation. `(d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0`

Explanation

`Let y=e ax cosbx .....(1)`

Differentiate both sides with respect to 'x'

`dy/dx =e ax(−bsinbx)+ae ax cosbx`

dy/dx =e ax [acosbx−bsinbx] ....(2)

Combining 1 and 2

= 0