Since, the given equation is unclear, we assume it as:
Solve(D2+4D+3)y=e−3x
Solution: Given equation is
(D2+4D+3)y=e−3x
A E is D2+4D+3=0
∴(D+1)(D+3)=0D=−1,D=−3CF=c1e−x+c2e−3xPI=(D+1)(D+3)1e−3x
put D=-3 in f(D) then
PI∴PIG.S.=01e−3x∴ method fails =(−3+1)(D−3+3)e−3x{1}=(−2)e−3xD1{1}=−2e−3xx=CF+PI
y=c1e−x+c2e−3x−2e−3xx
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