Question

у" — у' — х %3D 0 ...


Obtain the general solution unless otherwise instructed

Transcribed: у" — у' — х %3D0

Answer

We are given:

y'''-y'-x=0y'''-y'=x

Auxiliary equation is :

m3-m=0m(m2-1)=0m=0, 1, -1

Hence, 

CF= Compliment Function = c1e0x+c2ex+c3e-x=c1+c2ex+c3e-x

Now `will find the Particular Integral :

Here , F(x)=x

P.I=1f(D)F(x)           =1(D3-D)(x)           =1-D(1-D2)(x)           =-1D(1-D2)-1(x)                       =-1D(1+D2+D4)(x)           =-1D(x)           =-x22

Now, the General solution is = CF+PI= c1+c2ex+c3e-x-x22

 

 

Now, the General solution is = CF+PI= c1+c2ex+c3e-x-x22

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