A nonhomogeneous equation and a particular solution are given. Find a general so

Cabiolab

Cabiolab

Answered question

2021-09-26

A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation.
y+7y+12y=36x2+42x+6+20ex,yp(x)=ex+3x2
y(x)=?

Answer & Explanation

grbavit

grbavit

Skilled2021-09-27Added 109 answers

Step 1
The given nonhomogeneous is y+7y+12y=36x2+42x+6+20ex
The auxiliary equation is,
m2+7m+12=0
m2+4m+3m+12=0
m(m+4)+3(m+4)=0
(m+3)(m+4)=0
m=3,4
Step 2
Thus, the complimentary function is yc=c1e3x+c2e4x.
The given particular solution is yp(x)=ex+3x2.
Substitute yc=c1e3x+c2e4x and yp(x)=ex+3x2  y(x)=yc+yp.
y(x)=c1e3x+c2e4x+ex+3x2

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