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

\({y}={e}^{x}{\left({c}_{{1}} \cos{{2}}{x}+{c}_{{2}} \sin{{2}}{x}\right)}\), where c_1 and c_2 are arbitracy constant.

This differential equation has infinitely many solutions since there is no initial conditions to determine a particular solution.

\(r^{2}+2r+5=0\)

and has the roots r_1=1+2i and r_2=1-2i.

The general solution is given by

\({y}={e}^{x}{\left({c}_{{1}} \cos{{2}}{x}+{c}_{{2}} \sin{{2}}{x}\right)}\), where c_1 and c_2 are arbitracy constant.

This differential equation has infinitely many solutions since there is no initial conditions to determine a particular solution.