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I am studying nonlinear differential equations, and came across an interesting one on maple's help page.  I made a post about this equation already, but I have decided to make a new post because the topic is slightly different than from the previous post.

The topic of this post is:

"Can numerical methods and exact, implicit techniques find false solutions?"

To make the discussion clearer, the rest of this post can be found in the maple file I created.


I would like to create an animation of the solutions to a differential equation, but I can't get animation to work.  I copy and pasted

plots[animate]( plot, [A*sin(x), x=0..10], A=0..2 )

into maple, but the animation did not animate, and only plotted the result for A = 0.  I am using Maple 2019.  Any ideas?


I am trying to verify the general solution to the nonlinear ode

diff(y(x), x, x) = 1/y(x) - x*diff(y(x), x)/y(x)^2  (1)

Maple says this expression is invalid when I try to enter it using the button.  I can copy and paste this expression into maple, however, and it works fine.


I take the second derivative of the general solution, then use the solve(solution, diff(y(x),x,x) command to try to put the second derivative in the form of (1).  The result from this command does not match the original ode, but the odetest( ) funtion returns a value of zero. 


How do I "manually" verify this solution with maple?  I am investigating a certain type of equation, and my solution technique so far involves rewriting the equation into a different form (nonlinear PDE) and then solving the PDE.  I am building up maple skills to eventually do that.


For your reference, this equation is from a maple help page:




I would really appreciate some help with this,

Steve :)


I have managed to create the following plot.  It won't plot on the site's plotter:

fieldplot([1, y^2 + x], x = -10 .. 10, y = -6 .. 6, fieldstrength = fixed, color = abs(y^2 + x + 1))

I am trying to assign a colour gradient to the different vectors based on vector magnitude.  In the color option, I entered color= expresssion for the magnitude of the vectors


This only half worked.  It currently scales the colours such that the largest and smallest vectors are the same colour.  How do I assign a gradient such that the small magnitude vectors are one colour, and they then transition to another colour as their magnitude gets larger?



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