- #1
ver_mathstats
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Homework Statement
Solve the initial value problem
y1'=-13y1+4y2
y2'=-24y1+7y2
y1(0)=5, y2(0)=2
Homework Equations
The Attempt at a Solution
Here is what I have:
y'=[-13 4, -24 7]y
I change it to A=[-13 4, -24 7]
My eigenvalues are λ=-1 and λ=-5.
My basis are [1/3 1] and [1/2 1].
Now I have to find u'=Du, which is:
[u1', u2'] = [-1 0, 0 -5][u1, u2]
Which then yields:
u1'=-1u1
u2'=-5u2
With these solutions:
u1=C1ex
u2=C2e2x
Now I obtain y=Pu, which is:
y=[1/3 1/2, 1 1][C1ex, C2e2x]
y=[(C1ex/3) + (C2e2x/2), C1ex + C2e2x]
Now I have:
y1=(C1ex/3) + (C2e2x/2)
y2=C1ex + C2e2x
Apply initial conditions to obtain:
y1=(C1/3) + (C2/2)=5
y2= C1 + C2=2
I solved and obtained:
C1=28
C2=-26
y1=(28ex/3) - (26e2x/2)
y2=28ex - 26e2x
Would this be right or did I make a mistake?
Thank you.