Solve the following matrix differential equation: = Ax where A= [ 5 1 ; -2 -2] and x0 =[-3; 8]
Solve the given integral equation or integro-differential equation for y(t). t Y'ce)+ (t = v)y(v) dv=t, y(0) = 0 y(t) =
Solve the given integral equation or integro-differential equation for y(t). V'(t)+125] (t-v)/(v) dv=5t, y) = 0 125 ſe-vrye y()=
2 2 0 0 3" (12%) Solve the linear system x"(t) AX(t) with A 0 0 4 4 a) (406) Write down the characteristic equation of the coefficient matrix λ and solve its eigenvalues, . b) (8%) Find the four independent solutions of the system.
('T polnt) Solve the equation AX(D + BX)-1 = C for X. Assume that all matrices are n x n and invertible as needed. You can enter the inverse of a matrix A as A^(-1). X =
Solve the given integral equation or integro-differential equation for y(t). t y'(t)+27 [ct –v)y(v) dv= 4t, y(0)=0 0 y(t) =
5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' Ax. Find the directions of greatest attraction and/or repulsion 12 16 A= 8 12 Solve the initial value problem. x(t) 5.7.3 Solve the initial value problem x'(t) Ax(t ) for t2 0, with x(0) = (3,2). Classify the nature of the origin as an...
Solve the given integral equation or integro-differential equation for y(t). t y' (t) + 125 (t-vy(v) dv = 10t, y(O) = 0 0 y(t) = []
Solve the given integral equation or integro-differential equation for y(t). t y'(t) + (t-vly(v) dv = 5t, y(O) = 0 fe-vy y(t) =
Solve the given integral equation or integro-differential equation for y(t). t y'(t) + 27 [(t-vjy(v) dv=t, y(0) =0 0 y(t) =