Question: System of ODE's with Boundary Conditions




I am trying to solve the following system of ODE's given some initial and final conditions.

{diff(p1(t), t) = VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](2, x1(t))), VectorCalculus[`*`](2, vf)), VectorCalculus[`*`](p1(t), 1/VectorCalculus[`*`](R, C))), VectorCalculus[`*`](p2(t), 1/L)), diff(p2(t), t) = VectorCalculus[`-`](VectorCalculus[`*`](p1(t), 1/C)), diff(x1(t), t) = VectorCalculus[`+`](VectorCalculus[`-`](VectorCalculus[`*`](x1(t), 1/VectorCalculus[`*`](R, C))), VectorCalculus[`*`](x2(t), 1/C)), diff(x2(t), t) = VectorCalculus[`-`](VectorCalculus[`*`](x1(t), 1/L))}

I would like to impose the boundary conditions x1(tf)=x1f,x2(tf)=x2f,p1(tf)=0,p2(tf)=0


Is there a way to solve this other directly using pdsolve? I can trying to substitute my boundary conditions into the general solution and solve for the coefficients, but this yields extremely messy results (and I know the answers are relatively simple spirals).


More generally, I am interested in having a mix of initial and final conditions. Any examples of how to do that would be helpful too.





Please Wait...