The plot in the attached file only works if the complete function expression is entered. If only the function name is entered, no plot appears. What am I doing wrong?test.mw

Download test.mw

I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

Download testdgl5.mw

In the attached file, I want to transform (1) into (3) and back again (3) into (1). Attempts using CompleteSquare and expand in combination with other commands have failed. I would appreciate any advice.

dio1.mw

I recently read something in another forum about solving a simple ordinary differential equation as an initial value problem (file attached). An unexpected solution behavior was interpreted there as a weakness of the software. However, upon closer inspection, the cause is different, and as a software novice, I cannot determine it myself.

Therefore, my question is:

Is there a way, using Maple, to check the Lipschitz condition in the neighborhood of the initial value before starting the solution of an explicit first-order system of differential equations as an initial value problem?

DGL_test.mw

Having started learning Maple about a year ago as a beginner, and now having mastered my preferred area of ​​"ordinary differential equations" fairly independently, I'd like to explore "elliptic curves" in Maple. For practice, I've chosen two problems, for each of which I only know one solution:

y^2 = x^3  -51*x^2 + 867*x - 4792    (17;11)

y^2 - 2*y + 14 = 2*x^3 + 11*x^2 - 29*x - 17    (3;7)

My attempts using commands like "algcurves", "ThueSolve", and "parametrization" have failed. How does one approach such problems in Maple? I'm also particularly interested in the group-theoretically based graphical secant method.

(I'm familiar with the book by Silverman/Tate.)