F-1 (10 Points): A flying plane at (a,0) approaches an airport at (0,0), which means the...

   

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F-1 (10 Points): A flying plane at (a,0) approaches an airport at (0,0), which means the plan is a miles directly east of the airport. A steady south wind of speed w blows from south to north. While approaching the airport, the plane maintains a constant speed vo relative to the wind and maintains its heading directly toward the airport at all times. (0,0) Vo W (a,0) (1) Compute the plane's trajectories for (1) w > vo, (2) w = vo, (3) w<vo. (2 Pts/case) (2) Compute the total time to travel from (a,0) to (0,0) for one case: w<vo. (4 Pts) F-2 (10 Points): Use your favorite method to find the G.S. of the following DE: x²y" + xy' - 16y = x + x¯4 F-3 (10 Points): Use Laplace Transform method (6 Pts)) and another method (4 Pts) to find the P.S. of the following DES: (x" - a²x = exp(Bt) x(0) = x'(0) = 0 where a and ß are constants. You need to treat it differently for a = B and a B. Convolutions (if any) must be evaluated. F-4 (10 Points): Use Laplace Transform method (6 Pts) and another method (4 Pts) to find the P.S. of the following linear system of DES: 24 () = (₁²_4₁) ()+(Cost) with initial conditions (0) sin (+8)=() F-1 (10 Points): A flying plane at (a,0) approaches an airport at (0,0), which means the plan is a miles directly east of the airport. A steady south wind of speed w blows from south to north. While approaching the airport, the plane maintains a constant speed vo relative to the wind and maintains its heading directly toward the airport at all times. (0,0) Vo W (a,0) (1) Compute the plane's trajectories for (1) w > vo, (2) w = vo, (3) w<vo. (2 Pts/case) (2) Compute the total time to travel from (a,0) to (0,0) for one case: w<vo. (4 Pts) F-2 (10 Points): Use your favorite method to find the G.S. of the following DE: x²y" + xy' - 16y = x + x¯4 F-3 (10 Points): Use Laplace Transform method (6 Pts)) and another method (4 Pts) to find the P.S. of the following DES: (x" - a²x = exp(Bt) x(0) = x'(0) = 0 where a and ß are constants. You need to treat it differently for a = B and a B. Convolutions (if any) must be evaluated. F-4 (10 Points): Use Laplace Transform method (6 Pts) and another method (4 Pts) to find the P.S. of the following linear system of DES: 24 () = (₁²_4₁) ()+(Cost) with initial conditions (0) sin (+8)=()