Answer Happy

1. Using Laplace transform, solve the following simultaneous equations: 6e3t, = (D-2)x - (D+1)y (2D-3)x+ (D-3)y = 6e3t, given x = 3, y = 0 when t=0. 2. Using Laplace transform, solve the following simultaneous equations: уі 1 = 4y2-8 cos 4t, -3y1 -9 sin 4t, y1(0) = 0, y2(0) = 3. Y2 - 3. Using Laplace transform, solve the following simultaneous equations: y1 - 5y1 + 4y2 92 - 10yı + 7y2 2t -912, = -17t2 - 2t, y1(0)=2, y2(0)=0. 4. Using Laplace transform, solve the following simultaneous equations: y +3yi-y2 = u(t-1)et, ya + 4yı – 2y2 = u(t-1)e", y1(0)= 0, y2(0) = 3. 5. a). Show that the system of differential equations for the currents iz(t) and iz(t) in the following electrical network is A R E L L2 1 L1 di2 dt +R(12+i 3)=E(t), dig L2 dt +R(12+iz)=E(t). b). Solve the system in part (a) if R = 51,L1 = 0.012,L2 = 0.0125h, E = 100V, i2(0) = 0, and iz(0) = 0. 6. Solve the following pde by using Laplace transform: @w + 2x @w = 2x, w(x,0) = 1,w(0,t)=1. дх + δω 7. Solve the following pde by using Laplace transform: x dx w(0,t) = 0 ift20. д ot = xt, w(x,0) = 0 if x 20 and 8. Solve the following pde by using Laplace transform: ut + xu x = x, u(x,0) = 0 and u(0,t) = 0. 9. Solve the following pde by using Laplace transform: + out = x, u(x,0) = 0, u(0,t)=0. 10. Solve the following pde by using Laplace transform: + x ou = 0, u(x,0) = 0,u(0,t)= t.