(c) Given differential equation is m4+4=0 ⇒m4+4+4m2−4m2=0 ⇒(m2+2)2−(2m)2=0 ⇒(m2+2+2m)(m2+2−2m)=0 Now;(m2+2+2m)=0and(m2+2−2m)=0 m=−
4±√4−4×2
2
and m=
4±√4−4×2
2
=
−4±√4i2
2
and =
4±√4i2
2
=
−4±2i
2
and =
4±2i
2
=−2±i and =2±i ∴m=2±i,−2±i ∴CF=e−2x(c1cosx+c2sinx)+e2x(c3cosx+c4sinx) PI=0 ∴Complete solution, y = CF + PI y=e−2x(c1cosx+c2sinx)+e2x(c3cosx+c4sinx)