Given equation is-
(3D2−2D2+D−1)z=4e(x+y).cos(x+y)(D2+D−1)z=4e(x+y).cos(x+y)
Auxiliary equation is-
m2+m−1=0
m=2−1±1−4=2−1±3i
Complimentary function is-
CF=e−2x(c1cos23x+c2sin23x)
Particular integral is-
PI=D2+D−14ex+ycos(x+y)
=4ex+y(D+1)2+(D+1)−1cos(x+y)=4ex+yD2+3D+1cos(x+y)=4ex+y−1+3D+1cos(x+y)=4ex+y3Dcos(x+y)=−4e(x+y)×3sin(x+y)
Complete solution is-
y=CF+PI
y=e−2x(c1cos23x+c2sin23x)−4e(x+y)×3sin(x+y)
Comments
Leave a comment