solve (D^3-5D^2+7D-3)y=e^2x cosh x
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Mathematics
The A.E. is m^3-5m^2+7m-3=0
need an explanation for this answer? contact us directly to get an explanation for this answerOr m^2 (m-1)-4m(m-1)+3(m-1)=0
Or (m-1)(m^2-4m+3)=0
Or (m-1)(m-1)(m-3)=0
so m=1,1,3
Y_(C.F.)=(c_1+c_2 x)e^x+c_3 e^3x
Y_(P.I.)=
1/( 〖(D-1)〗^2 (D-3)) e^2x coshx=1/2 1/( (D-1)^2 (D-3) ) e^2x (e^x+
e^(-x))=1/2 1/( (D-1)^2 (D-3) ) (e^3x+e^x )
=1/2 1/( (D-1)^2 (D-3) ) e^3x+1/2 1/( (D-1)^2 (D-3) ) e^x
=1/8 1/(D-3) e^3x-1/4 1/(D-1)^2 e^x=1/8.x/1! e^3x-1/4.x^2/2! e^x
=1/8 xe^3x-1/8 x^2 e^x
Y_(G.S.)=(c_1+c_2 x) e^x+c_3 e^3x-1/8 x^2 e^x+1/8 xe^3x