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

crealolobk

crealolobk

Answered question

2021-12-16

Apply unknown coefficients to the following differential equation to solve it.
y +7y+6y=30

Answer & Explanation

Stella Calderon

Stella Calderon

Beginner2021-12-17Added 35 answers

Take a look at the differential equation.
y +7y+6y=30...(1)
(D2+7D+6)y=30 where D=d dx 
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
yc=c1ex+c2e6x

Medicim6

Medicim6

Beginner2021-12-18Added 33 answers

Can I get full answer, please. I think tha is not full.
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

So,
yp=Ax+B
yp=A,
yp=0
0+7A+6(Ax+B)=30
(7A+6B)+6Ax=30
6A=0
7A+7B=0
A=0 and B=5 (A=0),(7(0)+6B=30),(6B=30),(B=5):
yp=0(x)+5
=5
The general solution:
y=yc+yp
yc=c1ex+c2e6x+5

yc=c1ex+c2e6x

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