Hi,

I'm new at maple and have a problem/question with the rkf45 numerical ODE Solver.

At first, my computer need a lot of time to calculate an analytic solution.

Therefor, I use the numerical way.

I have the following second order ODE:

ODE:=m*((D@@2)(x))(t)+d*(D(x))(t)+k*x(t) = d*(eval(diff(y(x), x), x = t))+k*y(t)

where y(t) is a realy big piecewise function, defined by me.

My initial conditions are:

x(0) = 0, (D(x))(0) = 0

With dsolve, I get the solution x(t) and the first derivative x'(t). I'm able to plot them with odeplot.

But...

Problem 1:

I need also the second derivative x''(t).

On this page: http://www.maplesoft.com/support/help/maple/view.aspx?path=dsolve%2Frkf45there is an example (eq 13 and 14) where the second derivative is useable, but this doesn't work with my differential equation.

I have add

(D(D(x)))(0) = 0

to my initial conditions but then, I got the error that only 2 initial conditions are required.

What could I do, so that rkf45 returns also the second derivative?

Problem 2:

And in addition to this, I want to calculate with x(t), x'(t), x''(t) but I found no way to use them.

Only plots are possible.

If I reduce y(t) to a minimum, I can do everything with the analytic solution: plot, d/dt, d2/dt2, +, -, ...

I tried also to convert the procedure to a function but in this case, there is no way to derivate it.

Many thanks...