S sumrtym77 New member Joined Sep 12, 2008 Messages 17 Sep 29, 2008 #1 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.
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.
S sumrtym77 New member Joined Sep 12, 2008 Messages 17 Sep 30, 2008 #2 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).
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).
