Though Rkadapt is often the best candidate among
various integrators, this rule is not "Bible".
Here is, piecewise as a learning step. Easy to
form Rkadapt from there for this simple demo case.
From recollection, this example is from Mathematica 4.0.

All integrators exhibit increasing balistic error.

Jean

ODE Fehlberg 45.sm (80 KiB) downloaded 39 time(s).