ENGI 3424 Chapter 5 –
Demonstration of Maple for the series solutions of some ODEs,
using examples from the lecture notes.
Below are the commands from the Maple worksheet.
Open the worksheet in Maple to see the resulting expressions.
Only some of the output is displayed here.
ENGI 3424 Example 5.11.3
Series Solution of a Second Order Linear ODE (non-constant coefficients)
> with(DEtools):
> ode := (1-x^2)*diff(y(x),x,x) - 5*x*diff(y(x),x)
- 3*y(x) = 0;
> Order := 11;
> dsolve(ode, y(x), series);
In order to see the parts of the general solution more clearly,
apply a set of initial conditions.
The part of the solution multiplying y'(0) is:
> ics := y(0)=0, D(y)(0)=1;
> dsolve({ode, ics}, y(x), series);
The part of the solution multiplying y(0) is:
> ics := y(0)=1, D(y)(0)=0;
> dsolve({ode, ics}, y(x), series);
The exact solution requires methods beyond the scope of this course:
> dsolve(ode, y(x));
which can be rewritten as