Plotting two separate NDSolve solutions together

gsln = NDSolve[{eqnx1[t], eqny1[t], eqnz1[t], eqnx2[t], eqny2[t],
eqnz2[t], x1 == x10, y1 == y10, z1 == z10,.....
ParametricPlot[Evaluate[{(y1sln[t]/rc), (z1sln[t]/rc)}], {t, 0, end}]

Generally I am able to plot the y1 solution with the z1 solution. I would also like to overlap that plot with the y2 solution as well as the z2 solution. How would I go about writing the code to do so?

rc is used to normalize.

• Can you maybe give an actual example that other people can evaluate? – J. M. will be back soon Sep 6 '17 at 22:41

To combine two graphics in one frame, we need to use Show. Here I consider two random systems of differential equations, because you haven't provided any.

sol1[x0_?NumericQ] :=
First@NDSolve[{x'[t] == 0.2*(x[t] - x[t]*y[t]),
y'[t] == Sin[t - 4]*(x[t]*y[t] - y[t]), x == x0,
y == x0}, {x, y}, {t, 0, 20}];

sol2[U0_?NumericQ] :=
First@NDSolve[{U'[t] == 0.1*(U[t] - U[t]*V[t]),
V'[t] == Sin[t - 3]*(U[t]*V[t] - V[t]), U == U0,
V == U0}, {U, V}, {t, 0, 20}];

p1 = ParametricPlot[
Evaluate[{x[t], y[t]} /. sol1[#] & /@ Range[0.9, 1.8, 0.1]], {t, 0,
20}, PlotStyle -> Red, PlotRange -> {{0, 2.3}, {0, 2.6}}, Frame -> True];

p2 = ParametricPlot[
Evaluate[{U[t], V[t]} /. sol2[#] & /@ Range[0.9, 1.8, 0.1]], {t, 0,
20}, PlotStyle -> Green, PlotRange -> {{0, 2.3}, {0, 2.6}}, Frame -> True];

Show[{p1, p2}] • Yes that is exactly it, thank you! – Naflive2 Sep 6 '17 at 23:01