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!

 

[alphy]

To plot y''[x] vs. y[x], you can use the following code:

Plot[Evaluate[y''[x] /. s], {y[x], 0, 2}, PlotRange -> All]

This will plot y''[x] on the y-axis and y[x] on the x-axis. You can adjust the range of the plot by changing the values in the PlotRange option. Additionally, you can add any desired styling options to customize the appearance of the plot.