(* ::Package:: *)

K0[X_]=Integrate[1/q^3 Exp[-(q^2/6)X]BesselJ[3/2,q]^2,{q,0,Infinity},Assumptions->{X\[Element]PositiveReals}];
K[X_]=If[X>10^-4,#1,#2]&@@{
K0[X],
Normal@Series[K0[X],{X,0,1},Assumptions->{X\[Element]PositiveReals}]
};

D0[Fo_,\[CapitalLambda]_]=Fo \[CapitalLambda]^2;
Dinf[Fo_,\[CapitalLambda]_]=Fo \[CapitalLambda]^2 (1+45 (1-\[CapitalLambda]^2)/\[CapitalLambda]^2 Integrate[1/q^3 BesselJ[3/2,q]^2/(6+Fo \[CapitalLambda]^2 q^2),{q,0,Infinity},Assumptions->{Fo\[Element]PositiveReals,\[CapitalLambda]\[Element]PositiveReals}]);

sol[Fo_,\[CapitalLambda]_,tmax_]:=NDSolveValue[{1/2 X''[s]==15/4 Fo (1-\[CapitalLambda]^2)K[X[s]] Exp[-s],X'[0]==Fo \[CapitalLambda]^2,X[0]==0},X[s],{s,0,tmax}]
