Why Dsolve considers my equations' variables constants!?

clear all
Nx = 2; % number of state equations
Nu = 1; % number of control parameters
% x = sym('x%d', [1 Nx]);
% p = sym('p%d', [1 Nx]);
syms u t
syms x p [1 Nx]
% State equations
Dx(1) = x(2);
Dx(2) = -x(2) + u(1);
% Cost function inside the integral
g = 0.5*u(1)^2; 
% Hamiltonian
H = g;
for i = 1 : Nx
    H = H + p(i)*Dx(i);
end
% Costate equations
for i = 1 : Nx
    Dp(i) = -diff(H,x(i));
end
% solve for control u
du = diff(H,u);
sol_u = solve(du,u);
% Substitute u to state equations
for i = 1 : Nx
    Dx(i) = subs(Dx(i),u,sol_u);
end
% convert symbolic objects to strings for using 'dsolve'
% need ti automate this solving
clear x p
syms x(t) p(t) [1 Nx]
eqx = diff(x,t)==Dx

eqx(t) = 

eqp = diff(p,t)==Dp

eqp(t) = 

eq = [eqx,eqp];
sol_h = dsolve(eqx,eqp);

[Ibrahim Bakry]

these are the final diff. equations:

eq = [diff(x1(t), t) == x2, diff(x2(t), t) == - p2 - x2, diff(p1(t), t) == 0, diff(p2(t), t) == p2 - p1]

the solution of dsolve is:

sol_h =

struct with fields:

x2: C2 - t*(p2 + x2)

x1: C1 + t*x2

p1: C3

p2: C4 - t*(p1 - p2)

But the answer should be like:

x2: (C3*exp(t))/2 - C4 + (C2*exp(-t))/2

x1: (C3*exp(t))/2 - C4*t - C1 - (C2*exp(-t))/2

p1: C4

p2: C4 - C3*exp(t)

I got the first solution by dsolve(eq) in my script, the second solution i got by dsolve(diff(x1(t), t) == x2, diff(x2(t), t) == - p2 - x2, diff(p1(t), t) == 0, diff(p2(t), t) == p2 - p1) in the workspace

Where is the ptoblem?

Answer 1

[Torsten]

syms t x1(t) x2(t) p1(t) p2(t)
eq = [diff(x1, t) == x2, diff(x2, t) == - p2 - x2, diff(p1, t) == 0, diff(p2, t) == p2 - p1]

eq(t) = 

dsolve(eq)

ans = struct with fields:
    x2: (C3*exp(t))/2 - C4 + (C2*exp(-t))/2
    x1: (C3*exp(t))/2 - C4*t - C1 - (C2*exp(-t))/2
    p1: C4
    p2: C4 - C3*exp(t)

[Ibrahim Bakry]

Thank you Torsten, but my code goal is to not write index number manully x1 x2 p1 p2, so i used syms x(t) p(t) [1 Nx], and by defining Nx, the code generats the approprate number of parameters, but here the code did not responded as expected!

[Torsten]

You cannot create arrays of symbolic functions in MATLAB, and this would be necessary if you wanted to proceed as you try in your code:

https://uk.mathworks.com/matlabcentral/answers/504406-how-can-i-define-an-array-of-symbolic-functions

[Ibrahim Bakry]

Thank you, this was helpful