Question

solve the yč of D²(D²+4)=96x²+sin2x-k​

Answer 1

Answer:

f(D)=D⁴+4D²

A.F,f(m)=0

m⁴+4m²=0

m²(m²+4)=0

m²=-4

m=2i,-2i

so,m=0,0,2i,-2i

therefore,

yc=(c1+c2x)e^0x+e^0x(c3cos2x+c4sin2x)

=(c1+c2x)+c3cos2x+c4sin2x.