Find the general solution of the given differential equation. y''-2y'-3y

djeljenike 2021-10-02 Answered
Find the general solution of the given differential equation.
y2y3y=3tet2y3y=3tet
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Expert Answer

smallq9
Answered 2021-10-03 Author has 106 answers
First find solution of homogeneous problem.
r22r3=0r1,2=1,3 using quadratic formula
Homogeneous solution:
yc=c1et+c2e3t
Let Y=Atet+Bt2et because g(t)=3tet and from example 5 we know that Y=Atet is not enough to match the coefficients
Plug Y into starting equation to find particular solution:
(Atet+Bt2et)2(Atet+Bt2et)3(Atet+Bt2et)=3tet
(AetAtet+2BtetBt2et)2Aet+2Atet4Btet+2Bt2et3Atet3Bt2et=3tet
AetAet+Atet+2Bet2Btet2Btet+Bt2et2Aet+2Atet4Btt+2Bt2et3Atet3Bt2et=3tet
2A+At+2B2Bt+Bt22A+2At4Bt+2Bt23At3Bt2=3t
4A+2B+

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