> with(DEtools):
(this package must be open in order for Maple to understand the other
commands)
Example 2.2.1
> ode := diff(y(x),x,x) + 2*diff(y(x),x) - 3*y(x) = x^2 + exp(2*x);
> dsolve(ode, y(x));
Example 2.2.2
> ode := diff(y(x),x,x) + y(x) = tan(x);
> dsolve(ode, y(x));
Note: (1 + sin(x)) / cos(x) =
sec(x) + tan(x),
so that the answer from this command is consistent with the solution
in the lecture notes.
Example 2.2.3
> ode := diff(y(x),x,x) -2*diff(y(x),x) + y(x) = exp(x);
> ics := y(0)=0, D(y)(0)=1;
> dsolve({ode,ics}, y(x));
Example 2.2.4 - an ODE with non-constant coefficients
> ode := x^2*diff(y(x),x,x) -5*x*diff(y(x),x) + 8*y(x) = 3*x;
> dsolve(ode, y(x));
Example 2.4.1 - higher order ODE
> ode := diff(y(x),x$5) + 2*diff(y(x),x$4) - 3*diff(y(x),x$3)
- 4*diff(y(x),x,x) + 4*diff(y(x),x) = 8*x;
> dsolve(ode, y(x));
Example 2.4.2 - higher order ODE
> ode := EI*diff(y(x),x$4) = W;
> ics := y(0)=0, D(y)(0)=0, D(D(y))(L)=0, D(D(D(y)))(L)=0;
> dsolve({ode,ics}, y(x));
