- #1
middieman147
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Homework Statement
y''-4y'+4y=0 , y(1)=1 and y'(1)=1
The Attempt at a Solution
Auxiliary equation: r2-4r+4=0
I tried factoring 2 different ways:
(r-2)2=0
r=2,r=2
y1=e2t
y2=y1
y(t)=c1e2t+c2e2t
y(1)=c1e2+c2e2=1 ---eq(1)y'(t)=2c1e2t+2c2e2t
...c2=1/(2e2)-c1 ---eq(2)
sub eq(2) into eq(1) --> 1/2=1method 2:
r(r-4)=-4
r=-4, r=0
y(1)=c1e-4+c2=1 ---eq(1)
y'(1)=c1=-1/(4e-4)
sub eq(2) into eq(1) --> c2=5/4
solution equation:
y(t)=1/4(-1+5)
=1... which doesn't seem correct
i checked the solutions on wolframalpha and it solves it using the first method, but ends up with:
y1=c1e2t
y2=c2e2t *t
can someone explain to me why the extra t shows up in y2? Thanks.
Homework Statement
Homework Equations
The Attempt at a Solution
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