Linear equations of second order with constant coefficients. Find all solutions on (−∞,+∞).y−2y′+5y=0

The characteristic equation is given by
$r^2+2r+5=0$
and has the roots $r_1=1+2i$ and $r_2=1-2i.$
The general solution is given by
$y=e^x(c_1\cos 2x+c_2\sin 2x)$, where $c_1\text{ and }{c}_2$ are arbitracy constant.
This differential equation has infinitely many solutions since there is no initial conditions to determine a particular solution.