Question

Q.3 Solve the simultaneous differential equation-
dx dy
+ + 3x = sint;
dt dt
dx
+ y - x = cost.
dt​

Answer 1

y=sint-d dt (c1et - c2e- t)

y=sin t-c1et-c2e-t

DX+y=sinvt .............(1)

Dy+x=cost..........(2) where d/dt=D

multiply (1)by D

D2x+ DX=cost............(3)

Dy+x=cost..............(4)

subtracting (4(from(3) we get

D2x-x=0

AE is (D-1)=0

D=1-1

x= c 1 e t + c2