Solve the given differential equation by undetermined coefficients y''+7y'+6y=30

crealolobk 2021-12-16 Answered
Solve the given differential equation by undetermined coefficients
y+7y+6y=30
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Stella Calderon
Answered 2021-12-17 Author has 35 answers
Consider the differential equation
y+7y+6y=30...(1)
Rewrite the equation,(D2+7D+6)y=30 where D=ddx
Auxiliary equation is,
f(m)=0
m3+7m+6=0
m2+6m+m+6=0
m(m+6)+1(m+6)=0
(m+6)(m+1)=0
m=1,6
Hence the complementary solution is,
yc=c1ex+c2e6x
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Medicim6
Answered 2021-12-18 Author has 33 answers
Can I get full answer, please. I think tha is not full.
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RizerMix
Answered 2021-12-29 Author has 438 answers

Oh, sure, sorry
Apply the undetemined coefficient method to find the particular solution as follows:
yp=Ax+B
Find the first and second derivatives,
yp=A,
yp=0
Substitute these values in equation (1)
0+7A+6(Ax+B)=30
(7A+6B)+6Ax=30
Compare the coeficients of constant and x terms,
6A=0
7A+7B=0
Solve the above two equations,
A=0 and B=5 (A=0),(7(0)+6B=30),(6B=30),(B=5):
Hence the particular solution is,
yp=0(x)+5
=5
The general solution is,
y=yc+yp
yc=c1ex+c2e6x+5
Therefore, the required general solution is yc=c1ex+c2e6x

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