"In fact, Maple can now fully solve over 94% of the 55,979 entries in the Online Encyclopedia of Integer Sequences (OEIS) that that can be shown to satisfy a linear recurrence relation. "

I hope that the next version of Maple will have the last 6% completed.

Non-linear recurrence relation case we also we need it too.

Regards.

@0

Maple gave the correct answer, one of many solutions.

pdetest(sol, eqs);

{0}# OK

A picture of a a worksheet in not executable: it is not editable.

So no-one here can do anything but read it before making suggestions.

You should post worksheets(or Maple code).

@C_R 

Mathematica is more advanced for solving define integrals.

The task is impossible with the current data.

See here:

When a circle can be encircled around a quadrilateral and yet touch each polygon vertex, the quadrilateral is said to be cyclic. A quadrilateral is referred to as bicentric if it can be both inscribed and circumscribed on a pair of circles rhen you can use Bretschneider’s formula.

For the Case III use: 

dsolve(eqs, [p(t), y(t)])

a := solve(eq, [x]);allvalues(a);

@adam25185 

For me works fine.

Download integral.mw

Which integral is wrong ?

@Alfred_F 

See:

Download eq.mw

@Alfred_F 

If "text is difficult to read" clik right mouse button on picture and open image in new tab, then should work.

infolevel[isolve] := 5;

infolevel[solve] := 5;

isolve(x^2 - 12*x*y + 6*y^2 + 4*x + 12*y - 3)

#isolve: Warning: unable to find solution over the integers.

(solve(x^2 - 12*x*y + 6*y^2 + 4*x + 12*y - 3, {x, y}, useassumptions = true) assuming (x in integer, y in integer))

#Warning, solve may not respect assumed property 'integer' on 'x'.
#Warning, solve may not respect assumed property 'integer' on 'y'.

#{x = 6*y - 2 + sqrt(30*y^2 - 36*y + 7), y = y}, {x = 6*y - 2 - sqrt(30*y^2 - 36*y + 7), y = y}

Mathematica gives:

The integral diverges !!!

help("piecewise");

and "Enter" ?