I recommend you take a look at ParametricNDSolveValue
:
{xmin, xmax} = {0, 1};
sol = ParametricNDSolveValue[
{
-y1''[x] == -Exp[kk1 (y1[x] - y2[x])] +
Exp[-kk2 (y1[x] - y2[x])], -y2''[x] ==
Exp[kk1 (y1[x] - y2[x])] - Exp[-kk2 (y1[x] - y2[x])],
y1[xmin] == yy10,
y1[xmax] == yy11,
y2[xmin] == yy20,
y2[xmax] == yy21
},
{y1, y2},
{x, xmin, xmax},
{kk1, kk2, yy10, yy11, yy20, yy21}
]
Manipulate[
Plot[
Evaluate[Through[sol[k1, k2, y10, y11, y20, y21][x]]],
{x, xmin, xmax}, AxesOrigin -> {0, 0}, PlotRange -> All
],
{{k1, 1}, -1, 1},
{k2, -1, 1},
{{y10, 0}, -1, 1},
{y11, -1, 1},
{{y20, 0}, -1, 1},
{y21, -1, 1}
]
If you need numeric values for a particular set of x-values, you can get them like this:
xValues = Range[0, 1, 0.1]
yValues = Through[sol[1, 1, 0, 1, 1, 0][xValues]]
k1, k2
? How abouty1[0], y1'[0], y2[0], y2'[0]
? $\endgroup$ – Αλέξανδρος Ζεγγ Sep 13 '18 at 8:34