Solve the given differential equation by undetermined coefficients y''-14'+49y=35x+4

Margie Marx

Margie Marx

Answered question

2021-12-19

Solve the given differential equation by undetermined coefficients
y14+49y=35x+4

Answer & Explanation

Ana Robertson

Ana Robertson

Beginner2021-12-20Added 26 answers

Consider the differential equation
y 14+49y=35x+4...(1)
Rewrite the equation,(D214D+49)y=30 where D=d dx 
Auxiliary equation is,f(m)=0
m2-14m+49=0
(m-7)2=0
m=7,7
Hence the complementary solution is,
yc=c1e7x+c2e7x

otoplilp1

otoplilp1

Beginner2021-12-21Added 41 answers

Is it all answer?
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

no, here is the continuation of the solution
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)
0-14A+49(Ax+B)=35x+4
-14A+49Ax+49B=35x+4
(-14A+49B)+49Ax=35x+4
Compare the coefficients of constant and x terms,
49A=35
-14A+49B=4
Solve the above two equations,
A=57 and B=27 

(A=(35)/(49)),(-14(5/7)+49B=4),(-10+49B=4),(49B=14),(B=2/7):
Hence the particular solution is,
yp=57x+27
The general solution is,
y=yc+yp
yc=c1e7x+c2e7x+57x+27
Therefore, the required general solution is yc=c1e7x+c2e7x+57x+27

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?