how to solve $\displaystyle y''+(4i+1)y'+y=0$?
how to solve $\displaystyle y''+(4i+1)y'+y=0$?
The same way you solve any linear constant coefficient homogeneous equation. Use a trial solution of the form $\displaystyle y(x)=e^{\lambda x}$ get the characteristic equation which you solve, then the general solution is a linear combination of the solutions found this way (with the usual caveats for double roots).