$(7+8=15$ points$)$ For the following differential equation

$y^{\text{'}\text{'}}+2y^{\text{'}}+2y=0,$

please answer the following questions and show all work.

a$.$ Find the general real solution.

b$.$ Solve the following initial value problem $($hint: use Euler's form$).$

$y^{\text{'}\text{'}}+2y^{\text{'}}+2y=0,y(0)=0,y^{\text{'}}(0)=4$