I need help bad with a general solution!

[sumrtym77]

Determine a general solution of the initial-value problem, y'' + y' - 30 = 0 with y(0)=8, y'(0)=7. I need help getting started please.

 

[sumrtym77]

Is this right: r^2 + r - 30 = 0
(r-5)(r+6)
y(x)= c1 e^5x + c2 e^-6x
y(0)=8, so 8=c1 + c2, c1 = 8-c2
y'(0)=7, so 7=5c1 - 6c2, so, 7= 5(8-c2) - 6c2 , 7=40 - 11c2, c2=3, c1= 5

So, y(x)= 5e^(5x) + 3e^(-6x).

 

[royhaas]

It is correct.