Dao Tuat
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Can someone give me some help, or at least tell me if I'm on the right track with this?
Heres what I was given:
4y'' - 4y' - 3y=0
y(0)=1
y'(0)=5
Heres what I did:
(sorry about the c1 and c2, I don't know how to make them show up as subsript)
4(r^2) - 4r - 3 = 0
r = 3/2 r=-1/2
y = c1e^(3x/2) + c2e^(-x/2)
1 = c1 + c2
y'' = [3c1e^(3x/2)]/2 - [c2e^(-x/2)]/2
5 = 3c1/2 - c2/2
c2 = ±2sqrt(7) - 5
c1 = 1/(±2sqrt(7) - 5) = [±2sqrt(7)]/3 + 5/3
y = [(±2sqrt(7))/3 + 5/3]e(3x/2) + [±2sqrt(7) - 5]e(-x/2)
Does this seem at all right?
Heres what I was given:
4y'' - 4y' - 3y=0
y(0)=1
y'(0)=5
Heres what I did:
(sorry about the c1 and c2, I don't know how to make them show up as subsript)
4(r^2) - 4r - 3 = 0
r = 3/2 r=-1/2
y = c1e^(3x/2) + c2e^(-x/2)
1 = c1 + c2
y'' = [3c1e^(3x/2)]/2 - [c2e^(-x/2)]/2
5 = 3c1/2 - c2/2
c2 = ±2sqrt(7) - 5
c1 = 1/(±2sqrt(7) - 5) = [±2sqrt(7)]/3 + 5/3
y = [(±2sqrt(7))/3 + 5/3]e(3x/2) + [±2sqrt(7) - 5]e(-x/2)
Does this seem at all right?