4 Linear ODEs with constant coefficients - complex roots\ (a) Find the general real solution of the ODE\

y^('')+2y^(')+10y=0.

\ (b) Find the solution to the ODE\

y^('')+2y^(')+10y=sinx

\ that satisfies

y(0)=y^(')(0)=0

.\ Please make sure your final solutions in parts (a)-(b) do not contain any

i

.

4 Linear ODEs with constant coefficients - complex roots (a) Find the general real solution of the ODE y+2y+10y=0. (b) Find the solution to the ODE y+2y+10y=sinx that satisfies y(0)=y(0)=0