Symbolic three-equation system, three variables to first derivative of each variable in each equation

Hello, I have this symbolic equation system:

Eqn1 = A(t)*x(t) + B(t)*y(t) C(t)*z(t) + D(t)*dx(t)/dt + E(t)*dy(t)/dt + F(t)*dz(t)/dt == f1(t);

Eqn2 = G(t)*x(t) + H(t)*y(t) I(t)*z(t) + J(t)*dx(t)/dt + K(t)*dy(t)/dt + L(t)*dz(t)/dt == f2(t);

Eqn3 = M(t)*x(t) + N(t)*y(t) P(t)*z(t) + Q(t)*dx(t)/dt + R(t)*dy(t)/dt + S(t)*dz(t)/dt == f3(t);

Of course, I know the formulas of A(t)..S(t) as well as the formulas of f1(t), f2(t) and f3(t) (they are just way too long to copy-paste here)

Now, my goal is to determine the formulas of x(t), y(t) and z(t) and I have absolutely no idea how to proceed... Also, not sure if that helps, but all the equations are sin and cos functions.

Thanks a bunch for all of your help

Answer 1

[Walter Roberson]

You can use the Symbolic Toolbox dsolve() .

However, if the formula are complicated, it would be common for dsolve to not be able to find a solution. Differential equations can be difficult to solve symbolically.

[VincentLec]

Would converting the symbolic function to a MatLab Function using matlabFunction make it easier for Matlab to solve them? For example, what if I did

eqn11 = matlabFunction(eqn1)

eqn22 = matlabFunction(eqn2)

eqn33 = matlabFunction(eqn3)

before using dsolve().

[Walter Roberson]

No, dsolve() is strictly symbolic and matlabFunction is for creating numeric routines (e.g., routines you might use with one of the ode* functions.)

[VincentLec]

Ok, I'll try to see what I can do. Thanks!