Question

solve-(D²+D+1)=sin2x​

Answer 1

Answer:

This method is solve by linear differential equations

Step-by-step explanation:

step1- let r.h.s.=0,D=m,

then solve it,THEN now we have C.F.

step2- now for P.I.

1 /D²+D+1 ×SIN2X

PUT D=2

THEN

SIN2X/7

step3-C.F. + P.I. IS THE ANSWER

Answer 2

Step-by-step explanation:

(D²+D+1)y = Sin2x

A.E. - m² + m + 1 = 0

m = -1 + √1-4 / 2

m = -1 + √3i / 2

m = w , w²

C.F. = C1*e^wx + C2*e^w²x

P.I. = 1/(D²+D+1) * Sin2x

= 1 / (-4+D+1) * Sin2x {D² --> -a²}

= 1/(D-3) * (D+3)/(D+3) * Sin2x

= (D+3)/(D²-9) * Sin2x

= (D+3)/(-4-9) * Sin2x

= -1/13 {2Cos2x + 3Sin2x}

व्यापक हल y = C.F + P.I.

y = C1*e^wx + C2*e^w²x -1/13 {2Cos2x + 3Sin2x}