MATLAB: SOLVE LINEAR DIFERENTIAL EQUATION WITH ONE UNKNOWN

differential equationunknown

I have the system of the image, but i want to solve the exatly system but insted of a fixed number where the four goes, i would like to find the range of solutions but with the unknown where the four goes.

I would usually solve this with pencil and paper but my system is 6×6, Thanks in Advance.

AUTHOR edit:

Sorry i think my explanation was not clear, what i would like to solve this ->

eqn1 = du == 3*u + X*v;

eqn2 = dv == -X*u + 3*v;

where X is a parameter, and i would like to find the family of solution's in function of my parameter X.

Best Answer

syms u(t) v(t)
du = diff(u,t);
dv = diff(v,t);
eqn1 = du == 3*u + 4*v;
eqn2 = dv == -4*u + 3*v;
sol = dsolve([eqn1, eqn2])
sol = struct with fields:
    v: [1×1 sym]
    u: [1×1 sym]
sol.u
ans = 
sol.v
ans =

Related Solutions

MATLAB: I failed to solve 4 equation differential equation. I’m giving the code. the same code for two equation worked well. The point the program stuck is dsolve(ode1,ode2,ode3,ode4) or dsolve(odes) and never it finishes.

Your equations ode1 and ode4 actually contains linearly dependent terms which are

3*u + 4*v(ode1), 6*u + 8*v(ode4)

This situation brings about infinitely many solutions to your system, therefore actually a unique solution can not be found. For instance if you change your term into

6*u + 7*y

in ode4, you will see that a unique solution is quickly found.

MATLAB: Solve system of differential equations with vector input

In the derivation, let ‘a’ simply be an undefined constant, and define the initial conditions as 0 (unless you want them to be something else). Then in the solution, provide ‘a’ as a row vector to get the solution:

syms A B u(t) v(t) a
ode1 = diff(u,t) == A * (a - u);
ode2 = diff(v,t) == B * (u - v);
odes = [ode1; ode2];
[uSol(t), vSol(t)] = dsolve(odes, u(0)==0, v(0)==0)
% Above work fine; below don't
uF = matlabFunction(uSol);
vF = matlabFunction(vSol);
av = randn(1, 11);
resultu = uF(0:10, 1, 2, av); % t, A, B
resultv = vF(0:10, 1, 2, av);

This evaluates them as functions of whatever you want to define ‘a’ to be.

Best Answer

Related Solutions

MATLAB: I failed to solve 4 equation differential equation. I’m giving the code. the same code for two equation worked well. The point the program stuck is dsolve(ode​1,ode2,ode​3,ode4) or dsolve(odes) and never it finishes.

MATLAB: Solve system of differential equations with vector input

Related Question

MATLAB: I failed to solve 4 equation differential equation. I’m giving the code. the same code for two equation worked well. The point the program stuck is dsolve(ode1,ode2,ode3,ode4) or dsolve(odes) and never it finishes.