MATLAB Code:
close all
clear
clc
syms x(t) y(t) s(t)
Dx = diff(x, t); % x'(t)
D2x = diff(x, t, 2); % x''(t)
Dy = diff(y, t); % y'(t)
D2y = diff(y, t, 2); % y''(t)
Ds = diff(s, t); % s'(t)
D2s = diff(s, t, 2); % s''(t)
fprintf('Part
(a)\n------------------------------------\n')
ODE = [Dx == y + t, Dy == 2 - x + t];
Sol = dsolve(ODE);
fprintf('x(t) = '), disp(simplify(Sol.x))
fprintf('y(t) = '), disp(simplify(Sol.y))
fprintf('\nPart
(b)\n------------------------------------\n')
ODE = [Dx == s - x, Dy == -y - 3*x, Ds == -2*s];
Sol = dsolve(ODE);
fprintf('x(t) = '), disp(simplify(Sol.x))
fprintf('y(t) = '), disp(simplify(Sol.y))
fprintf('s(t) = '), disp(Sol.s)
fprintf('\nPart
(c)\n------------------------------------\n')
ODE = [D2x == Dx - x - y, D2y == -x - Dy - y - Ds, D2s ==
-9*s];
Sol = dsolve(ODE);
fprintf('x(t) = '), disp(simplify(Sol.x))
fprintf('y(t) = '), disp(simplify(Sol.y))
fprintf('s(t) = '), disp(simplify(Sol.s))
fprintf('\nPart
(d)\n------------------------------------\n')
ODE = [D2x == Dx - x - y, D2y == -x - Dy - y - Ds, D2s ==
-9*s];
Cond = [x(0) == 1, Dx(0) == 0, y(0) == -1, Dy(0) == 0, s(0) == 1,
Ds(0) == 0];
Sol = dsolve(ODE, Cond);
fprintf('x(t) = '), disp(simplify(Sol.x))
fprintf('y(t) = '), disp(simplify(Sol.y))
fprintf('s(t) = '), disp(simplify(Sol.s))
Output:
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