Solution: The auxiliary equation for the given differential equation is \[ m^2 - 5m + 6 =0. \] The roots of the above differential equation are \[ (m-2)(m-3) = 0 \implies m=2,3. \] Therefore, the solution of the given differential equation will be \[ c_1e^{2x} + c_2e^{3x}, \] where $c_1$ and $c_2$ are arbitrary constants.