Symbolic system of odes

Hey! So, I've been working on this physics problem where I face a system of four coupled differential equations which I can't seem to find the answer to

    TT0 = 0; %initial release angle Theta
    l0 = 1; %initial left line length (in meters)
    m = 1;
    M = 3;
    R = 0.3;
    g = 9.8;
    mu = 0.5;
    syms t Ti(t) Tx(t) TT(t) l(t);
    ode1 = (M*g) - Tx == -M*(diff(l,t,2)+R*diff(TT,t,2));
    ode2 = m*g*sin(TT) - Ti == m*(R*diff(TT,t,2)-l*(diff(TT,t))^2 + diff(l,t,2));
    ode3 = m*g*cos(TT) == m*(R*(diff(TT,t))^2 + 2*diff(l,t)*diff(TT,t) + l*diff(TT,t,2));
    ode4 = Tx == Ti*exp(mu*(pi/2 + TT));
    odes = [ode1; ode2; ode3; ode4];
    conds = [TT(0) == TT0; l(0) == l0;Ti(0) == 0; Tx(0) == M*g];
    D = dsolve(odes,conds);

Here's the code I've written. There are four equations and four indeterminates but I get this error when I run the code:

"

Error using mupadengine/feval (line 163)

Cannot reduce to the square system because the number of equations differs from the number of indeterminates.

Error in dsolve>mupadDsolve (line 332)

T = feval(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 193)

sol = mupadDsolve(args, options);

Error in Untitled (line 16)

D = dsolve(odes,conds)

"

I've searched the internet and altered my code several times but it didn't seem to work. I'll highly appreciate any kind of help. Thanks.

[Torsten]

For a 2nd order ODE, you need two initial conditions...

[Web Junkie]

@torsten I actually have 4

[Torsten]

I think you will have to manipulate your equations a bit before solving.

Insert

Tx = Ti*exp(mu*(pi/2 + TT));

into ode1.

Multiply ode2 by

exp(mu*(pi/2 + TT)) 

and then subtract the modified "ode2" from ode1. Then Ti cancels out.

Now use the result of your subtraction and ode3 to solve for TT and l. You will have to prescribe two initial conditions for TT and two initial conditions for l.

After this, Tx automatically follows from the original ode1 and Ti from the original ode4.

It is very unlikely that TT and l can be determined using "dsolve".

You will have to use ode15i, I guess.

[Web Junkie]

@Torsten Now that was a really good idea. I'll try but the things is that I'm not so good with numeric solutions but thanks for helping me elliminate Ti.

[darova]

Can you please show your equations in LaTeX or picture? Can't understand what is written there