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zak8000
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Homework Statement
y''+4y'+4y= t+exp(-2t)
find the general solution for the differential equation
Homework Equations
The Attempt at a Solution
general solution is sum of complementary function and particular integral
frist finding complementary function
y''+4y'+4y=0
let y=Aexp(mt)
y'=mA=exp(mt)
y''=(m^2)A=exp(mt)
substitute back and get
((m^2)+4m+4)Aexp(mt)=0
m=-2,0
so complementary function:
y=Aexp(-2t)+B
now find particular integral
y''+4y'+4y=t+exp(-2t)
try
y=a+bexp(-2t)
y'=-2bexp(-2t)
y''=4bexp(-2t)
substitute back and get
4bexp(-2t)-8bexp(-2t)+4(a+bexp(-2t))=t+exp(-2t)
(4+4-8)bexp(-2t)+4a=t+exp(-2t) !
so a = t/4 but b will always go to zero i don't know where my mistake is