Question

Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of (det2A)? (4 Points) e) Given: U2 + V2 + Y2 + 2x = 0 Find (aUlaX)x (10 Points) y' y- Method of Frobenius (8 Points) g) Solve the system of equations: (dy/dx) + z-e L(dx/dt) - x + (dv/dt) + (dz/dt)-0 (6 Points) x 2y (dz/dt-e h)Find: S/2+5/3 (6 Points) S2 4S 6 i) Use the Method of Digonalization: (dx/dt)-x+y+ e L(dy/dt)-x +y +e" (18 Points) (dz/dt) -3z+ te'

Answer 1

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