Plotting y''[x] vs. y[x] in Mathematica with NDSolve

[Niles]

Hi

Say I solve the following differential equation in Mathematica:

s = NDSolve[{y''[x] + Sin[y[x]] y[x] == 0, y[0] == 1, y'[0] == 0}, y, {x, 0, 30}]
Plot[Evaluate[{y[x], y'[x], y''[x]} /. s], {x, 0, 30}, PlotStyle -> Automatic]

The last line plots the solutions vs. x, but how can I plot e.g. y''[x] vs. y[x]?


Niles.

 

[kai_sikorski]

ParametricPlot[Evaluate[{y[x], y''[x]} /. s], {x, 0, 30}]

 

[Niles]

Hi

Thanks for that. Whenever I try and alter the PlotRange, it changes both x and y. I guess that is reasonable, since it is a parametric plot. But is there any way for me to determine the range of x and y independently?Niles.

 

[Niles]

PlotRange -> {{0, 10}, {0, 5}} works. Thanks!