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

Asked by VincentLec on 13 Jun 2016
Latest activity Commented on by VincentLec on 13 Jun 2016
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

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1 Answer

Answer by Walter Roberson
on 13 Jun 2016
 Accepted Answer

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.

  3 Comments

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

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