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Alfred_F

Mr. Alfred Flaßhaar

595 Reputation

11 Badges

1 years, 336 days
Brandenburg, Germany
Contact Alfred Flaßhaar
As a retired individual with degrees from German universities in mathematics/analysis and structural engineering, I spent my professional life in responsible positions in research, teaching, and practical application, working on the mathematical modeling of states and processes in real-world systems. Now I have the time to explore interesting mathematical problems using Maple. It is my professional curiosity that drives me.

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These are questions asked by Alfred_F

Recalcitrant differential equation...

Alfred_F 595 Maple 2026
ode dsolve differential-equations
July 29 2026
3 2

In the attached file, I'd like to solve an ODE as an exercise. Only the "series" option yielded a solution. How can the length of the result series be controlled? Is there a package that leads to a "closed" solution – even using well-known transcendental functions?

restart

ode := (1+f(x))*(diff(f(x), x, x)) = 1+x

(1+f(x))*(diff(diff(f(x), x), x)) = 1+x

 (1)

ics := f(0) = 1, (D(f))(0) = 0

f(0) = 1, (D(f))(0) = 0

 (2)

dsolve({ics, ode}, f(x), series)

f(x) = series(1+(1/4)*x^2+(1/12)*x^3-(1/192)*x^4-(1/240)*x^5+O(x^6),x,6)

 (3)

``

Download test.mw

How is a cyclic command sequence program...

Alfred_F 595 Maple
programming recursion
July 25 2026
3 2

In the attached file, I would like to calculate the expressions for the function f(n,x) using a recursion for a given index range, e.g., n=3..15. I would appreciate any advice on this.
 

> 

NULL
> 

restart;
> 

kernelopts(version);

`Maple 2026.1, X86 64 WINDOWS, Jun 04 2026, Build ID 2018217`

 (1)
> 

f(1,x):=x;

x

 (2)
> 

f(2,x):=2*x + 2*sin(x);

2*x+2*sin(x)

 (3)
> 

f(n,x):=2*f(n-1,x)-f(n-2,x)+2*sin((n-1)*x)/(n-1);

2*f(n-1, x)-f(n-2, x)+2*sin((n-1)*x)/(n-1)

 (4)
> 

f(3,x):=eval(f(n,x),n=3);

3*x+4*sin(x)+sin(2*x)

 (5)
> 

f(4,x):=eval(f(n,x),n=4);

4*x+6*sin(x)+2*sin(2*x)+(2/3)*sin(3*x)

 (6)
> 

NULL
> 

NULL


 

Download test24c.mw

 

How to solve the equation?...

Alfred_F 595 Maple
solve
July 07 2026
2 1

I would like to solve an equation in the attached file as an exercise. I am looking for all solutions - including the complex ones. This is easily done using "derive". There are six solutions:

restart

solve(2^x*(2+sqrt(3))^x-2*(1+sqrt(3))^x = 2, x)

RootOf(2^_Z*(2+3^(1/2))^_Z-2*(1+3^(1/2))^_Z-2)

 (1)

NULL

edited "test":

test.mw

Five are complex, and the single real solution can be guessed simply by taking a close look. I am unable to obtain the complete solution in Maple; I cannot find my mistake and would appreciate some advice.

Calculation of the integral and Green...

Alfred_F 595 Maple 2026
integration greens-theorem
June 20 2026
3 8

The integral shown in the attached file "test" was posted on another forum for calculation. I unsuccessfully attempted to apply Green's theorem in Maple and—as befits a Maple beginner—failed. Does Maple offer a sequence of commands to carry this out? I would appreciate some advice. If this is possible, I would then tackle the line integral using the residue theorem.

> 

restart

NULL

NULL

 

``

Download test.mw

Lattice Points and Lattice Polygon...

Alfred_F 595 Maple
geometry plotting
June 01 2026
4 15

For exercises involving Pick's Theorem, I need grid points within a Cartesian coordinate system. How can "all" grid points - at least within the first quadrant - be generated without the tedious manual entry of integer coordinates? Is it possible to draw grid polygons as closed polylines simply by clicking on the grid points? (BTW: At the moment, this works well in the good old "Cabri.")
My search within the "Help" section (using terms such as plot, grid, mesh, lattice, etc.) proved unsuccessful.

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