a=1; eqns[a_?NumericQ, r_?NumericQ, gamma_?NumericQ] :=
{Derivative[4][f][y] -
2 Derivative[2][f][y] a^2 + a^2 (-r y + a^2) f[y] == 0, f[0] == 0, Derivative[3][f][0] - Derivative[1][f][0] a^2 == 0,
Derivative[1][f][0] == 1, Derivative[2][f][0] == gamma}
sol[a_?NumericQ, r_?NumericQ, \[Gamma]_?NumericQ] := NDSolve[eqns[a,
r, \[Gamma]], f, {y, 0, 1}, Method -> "BDF", MaxSteps -> Infinity,
InterpolationOrder -> All]
eval = sol[1, 2, 3][[1, 1]]
ff = f /. eval
Plot[ff[y], {y, 0, 1}]
Hi everyone, I would know how I can find the value of ‘r’ using
FindRoot and plot it (r,a) with this conditions target y=1,f[1] = 0,
f’'[1] = 0. Thanks a lot.