Question

Obtain the complementary function and particular integral of (6M) (D²+4) y=e^3+sin2x+cos2x​

Answer 1

Answer:

given eqn, (D²+4)=e³+sin2x+cos2x

here,f(D) =D²+4

A.F,f(m)=0

m²+4=0

m²=-4

m²=-2²

m=2i,-2i

so,yc (complimentary fn)=c1cos2x+c2sin2x

now yp=1/f(D) .Q

yp= 1

___ (e^3x+sin2x+cos2x)

D²+4