- #1
ihumayun
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Homework Statement
Find y as a function of x if
y'''−11y''+28y'=0 y(0)=1 y'(0)=7 y''(0)=2
I have one attempt left on this question. Could someone verify my answer for me?
Homework Equations
The Attempt at a Solution
(use t as lamda)
t^3-11t^2+28t=0
t(t-4)(t-7)=0
t= 0, 4, 7
y = C1 e^(4x) + C2 e^(7x) + C3
1 = C1 (1) + C2 (1) + C3 ...(1)
y' = 4 C1 e^(4x) + 7 C2 e^(7x)
7 = 4 C1 + 7 C2 ... (2)
y'' = 16 C1 e^(4x) + 49 C2 e^(7x)
2 = 16 C1 + 49 C2 ...(3)
Using (2) and (3) to solve for C1 and C2:
28 = 16 C1 + 28 C2 --> (2)*2
2 = 16 C1 + 49 C2 ---> (3)
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26 = -21 C2
C2 = (26/-21)
2 = 16 C1 + 49 (-26/21) ... (3)
C1 = 47/12
1 = -26/21 + 47/12 + C3
C3 = 1+ 26/21 - 47/12
C3 = 121/84
y = (47/12)e^(4x) - (26/21) e^(7x) +121/84