# Solving DE with shooting method

NDSolve[{(2 π ϵ Cos[2 π x] Sech[κ + ϵ κ Sin[2 π x]]^2 (2 κ + 2 ϵ κ Sin[2 π x] -
Sinh[2 κ (1 + ϵ Sin[2 π x])]))/(κ (1 + ϵ Sin[2 π x])^2) +
4 π ϵ Cos[2 π x] (1 + ϵ Sin[2 π x])^2 Derivative[1][p][x] +
2/3 (1 + ϵ Sin[2 π x])^3 (p'')[x] == 0,
p[0] == 0, p[1] == 0}, p, x,
Method -> {"Shooting", "StartingInitialConditions" -> {p[0] == 0, p'[0] == 1}}]


On running this code, the error getting displayed is

NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.

• In the environment click on the triple dot symbol and click on the entry NDSolve::ndnum. There is instruction that will help You further. For me the instruction tells, give a value to the parameters with With! Commented Dec 30, 2023 at 15:10
• @Trueee Parameter \[Epsilon],\[Kappa] are undefined. Check the form of the derivatives in your ode, should be p'[x],p''[x] Commented Dec 30, 2023 at 17:23

Try ParametricNDSolveValue (I corrected the derivatives ...)
P = ParametricNDSolveValue[