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# DSolve[ ] returns Input again?

Posted 3 years ago
 I am solving a differential/algebra system of equations (actually the Euler-Lagrange case). The thing is that when I run the command, it does not returns error nor answer, it just repeats the very same line I write but with the expressions expanded. I attach the notebook. Thank you so much!!! I really appreciate your help. Attachments:
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Posted 6 months ago
 First I rationalized your equations. Then I noticed that the equation for x[t] separates and is very easy. Replacing this solution into the equation for z[t] I saw that this becomes singular for a value of t between 0 and 1: F = Derivative[3][x][ t]^2 + ((-3*(-0.75 + x[t])* Derivative[1][x][ t]^3)/(0.48999999999999994 - (-0.75 + x[t])^2)^(3/ 2) - (3*(-0.75 + x[t])^3* Derivative[1][x][ t]^3)/(0.48999999999999994 - (-0.75 + x[t])^2)^(5/ 2) - (3*Derivative[1][x][t]*Derivative[2][x][t])/ Sqrt[0.48999999999999994 - (-0.75 + x[t])^2] - (3*(-0.75 + x[t])^2*Derivative[1][x][t]* Derivative[2][x][ t])/(0.48999999999999994 - (-0.75 + x[t])^2)^(3/2) + 6*Derivative[1][z][t]* Derivative[2][z][t] - ((-0.75 + x[t])*Derivative[3][x][t])/ Sqrt[0.48999999999999994 - (-0.75 + x[t])^2] + 2*z[t]*Derivative[3][z][t])^2 // Rationalize // Simplify; bdryX = {x[0] == 0, x[1] == 1, x'[0] == 0, x''[0] == 0, x'[1] == 0, x''[1] == 0}; bdryZ = {z[0] == 0.3162, z[1] == 0.5884, z''[0] == 0, z'[1] == 0, z''[1] == 0} // Rationalize; eqs0 = Solve[{D[D[F, z'''[t]], {t, 3}] + D[D[F, z'[t]], {t, 1}] == D[D[F, z''[t]], {t, 2}] + D[F, z[t]], D[D[F, x'''[t]], {t, 3}] + D[D[F, x'[t]], {t, 1}] == D[D[F, x''[t]], {t, 2}] + D[F, x[t]]} // Simplify, D[{x[t], z[t]}, {t, 6}]][[1]] /. Rule -> Equal // Simplify; eqx = eqs0[[1]] solx = DSolve[Join[{eqx}, bdryX], x, t][[1]] eqz = eqs0[[2]] /. solx eqz /. Solve[Denominator[eqz[[2]]][[1, 1]] == 0 && 0 < t < 1][[1]] // Simplify 
Posted 6 months ago
 I met the same problem today. I put the code into wolfram online, I get a result. But my desktop version of Mathematica returned the input to me exactly. There must be a bug.
Posted 3 years ago
 It is a nonlinear boundary value problem, unlikely to have a closed-form solution. Try NDSolve.