Question $(1)$: Verify that the function is a solution of the differential equation:

Function, dif equation

a$)y=C{e}^x,$ y$\text{'}=5$y

b$)y=e^{-2x},3$y$\text{'}+5$y$=-{}^{}$e?-2x

c$)y=C_{1}sinx-C_{2}cosx,y^{\text{'}\text{'}}+y=0$

d$)y=C_1{e}^{-x}cosx+C_2{e}^{-x}sinx,y^{\text{'}\text{'}}+2y^{\text{'}}+2y=0$

Please do understandable writing and explain step by step, thank you so much :)