Question

(d²+d)y=(x²+2x+4) please find answer for me​

Answer 1

Answer:

I hope this is helpful for you

Step-by-step explanation:

We have to solve (D2−4D+1)y=x2

The characteristic equation is p2−4p+1=0

⇒p=24±16−4=24±23=2±3

Thus Complementary function C.F.=Ae(2+3)x+Be(2−3)x

Particular integral P.I.=D2−4D+11(x2)

                                        =[1−(4D−D2)]−1(x2)

                                        =[1+(4D−D2)+(4D−D2)2+...](x2)

                                        =[1+4D+15D2+...](x2)

                          ∴P.I.=x