# Unable to find initial conditions in ParametricNDSolveValue for a system of three ODEs

In my code

$PrePrint = # /. {Csc[z_] :> 1/Defer@Sin[z], Sec[z_] :> 1/Defer@Cos[z], Cot[z_] :> Defer@Cos[z]/Defer@Sin[z], Csch[z_] :> 1/Defer@Sinh[z], Sech[z_] :> 1/Defer@Cosh[z], Coth[z_] :> Defer@Cosh[z]/Defer@Sinh[z]} &; \[Epsilon] := 1/100 L := 10 d := 1 \[Phi] := \[Pi]/4 \[Chi]m := \[Pi]/6 \[Chi]p := \[Pi]/3 \[Alpha]p := 1 N5 := 1 M5 := 1 N3 := 100 \[CapitalDelta]N3 := 4 gYM := 10 \[Delta] = 1/2 Log[1/( gYM^2 N5^2 (2 N3 - \[CapitalDelta]N3)) (2 gYM^2 N3 N5^2 + 4 \[Pi]^2 \[CapitalDelta]N3^2 + Sqrt[(2 gYM^2 N3 N5^2 + 4 \[Pi]^2 \[CapitalDelta]N3^2)^2 - gYM^4 N5^4 (4 N3^2 - \[CapitalDelta]N3^2)])]; \[Alpha] = -(M5/4) Cosh[\[Delta]] + Sqrt[(\[Pi]^2 N3)/gYM^2 + M5^2/16 Cosh[\[Delta]]^2]; \[Alpha]h = (gYM^2 \[Alpha])/(4 \[Pi]); h1 = \[Alpha]p (-I \[Alpha] Sinh[v] - M5/4 Log[ Tanh[(I \[Pi])/4 - (v - \[Delta])/ 2]]) + \[Alpha]p (I \[Alpha] Sinh[vb] - M5/4 Log[Tanh[-((I \[Pi])/4) - (vb - \[Delta])/2]]); h2 = \[Alpha]p \[Alpha]h (Cosh[v] + Cosh[vb]); w = D[D[h1 h2, vb], v]; F1 = 2 h1 h2 D[h1, v] D[h1, vb] - h1^2 w; F2 = 2 h1 h2 D[h2, v] D[h2, vb] - h2^2 w; subv = {v -> x[x2] + I y[x2], vb -> x[x2] - I y[x2]}; f42 = 2 ((F1 F2)/w^2)^(1/4) /. subv; \[Rho]2 = 4 (F1 F2 w^2)^(1/4)/(h1 h2) /. subv; Lag = \[Sqrt](f42/ u[x2]^2 (f42/u[x2]^2 u'[x2]^2 + f42/ u[x2]^2 + \[Rho]2 (x'[x2]^2 + y'[x2]^2))); pu = D[Lag, u'[x2]]; equ = D[Lag, u[x2]] - D[D[Lag, u'[x2]], x2]; eqx = D[Lag, x[x2]] - D[D[Lag, x'[x2]], x2]; eqy = D[Lag, y[x2]] - D[D[Lag, y'[x2]], x2]; pdes = {equ == 0, eqx == 0, eqy == 0}; x20 = -d Cos[\[Phi]]; x21 = +d Cos[\[Phi]]; u0 = Sqrt[\[Epsilon]^2 + (L - d Sin[\[Phi]])^2]; x0 = ArcSinh[(L - d Sin[\[Phi]])/\[Epsilon]]; y0 = \[Pi]/2 - \[Chi]m; u1 = Sqrt[\[Epsilon]^2 + (L + d Sin[\[Phi]])^2]; x1 = ArcSinh[(L + d Sin[\[Phi]])/\[Epsilon]]; y1 = \[Pi]/2 - \[Chi]p; L - d Sin[\[Phi]] \[GreaterSlantEqual] 0 in = {u0, x0, y0} // N out = {u1, x1, y1} // N {x20, x21} s = ParametricNDSolveValue[ Flatten[{pdes, u[x20] == u0, u'[x20] == p, x[x20] == x0, x'[x20] == q, y[x20] == y0, y'[x20] == r}], {u, x, y}, {x2, x20, x21}, {p, q, r}, Method -> {"EquationSimplification" -> "Residual"}]  where I try to solve a system of differential equations with free first derivatives in the initial points produces the following message ParametricNDSolveValue::icfail: Unable to find initial conditions that satisfy the residual function within specified tolerances. Try giving initial conditions for both values and derivatives of the functions. when I set values for the first derivatives (parameters), for example (my goal is to fix these values in order to attain a second fixed point) s[300, 2, -1]  I mean, the code solved "simbolically" the system, and fixing the derivatives produces the error? You can see that I impose Method -> {"EquationSimplification" -> "Residual"} since the system is large and everything is mixed. Looking for an answer in Documentation I got This message is generated when NDSolve is unable to find initial conditions that satisfy the equations. and An error occurs because these equations do not have a solution Notice also that this problem is related to a question I asked before in Solving a simple BVP (with an error) when only had one equation and tried to prove a simple case. The methode there worked to find the first derivative that allows to attain a second point. • Looking at your setting for $PrePrint, you might want to try SetSystemOptions["SimplificationOptions" -> "AutosimplifyTrigs" -> False]; instead. – J. M.'s ennui Mar 26 '18 at 23:47
• @J.M. Thanks, now another problem appeared, it takes infinite time to get a result. I think it meas the code doesnt find any singularities and run correctly. – Patrick El Pollo Mar 27 '18 at 20:06