calculus help plz?

Question

Find the general solution. Give the real form. (2nd order linear diff eq)

1) 2y" + 3y' = 0

2) y" − y' − 30y = 0

show work/steps plz..thanks!

Answer 1

2r^2 +3r=0 r=0 and r= -3/2
y= C1 +C2 e^-3/2x
r^2-r-30=0
r=((1+-sqrt(121))/2 r= 6 and r= -5
y= C1 e^-5x +C2 e^6x