I would like to solve a differential equation using a series expansion in the attached file for practice purposes. How can the number of terms in the series solution be adjusted? I couldn't find anything about this in the help text.
BTW:
The differential equation is exceptionally tricky for a symbolic solution ;-) .

testdgl-1.mw

In the attached file, I have solved an ordinary differential equation implicitly. The simplification that is obviously possible using "simplify" is not being performed. Furthermore, "implicitplot" is not working either. I would appreciate some advice.

test.mw

As an exercise to further familiarize myself with Maple, I would like to calculate the definite integral specified in the attached file. The integrand has an antiderivative, and a source lists the value of the integral as approximately 0.57... Based on the plot, this value is plausible according to a simple estimate (Pi/2 * 0.8 / 2). Following standard practice taught in school, I therefore calculated the difference between the values ​​of the antiderivative at the limits of integration. Surprisingly, the result is a complex number. What am I doing wrong? Did the internal Maple calculation switch to complex principal values?

testint5.mw

For the purpose of practicing with Maple, I have worked on a definite integral in the attached file. I found it on the Internet. According to a side calculation, it can only be calculated using famous special functions or series expansions. That is why I am only interested in the numerical evaluation here. According to auxiliary calculations, it can only be computed using famous special functions or a series expansion. It is known that the series expansion of the antiderivative converges very rapidly. Therefore, for comparison purposes, I calculated the values ​​for integration limits of 10 and 100 instead of infinity. In the first graph, the two result curves appear to coincide perfectly. Is there a way to zoom in locally - like using a magnifying glass - to make the difference in the ordinate values ​​visible?

Download testint3.mw

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?

Download test.mw