The solution of the initial value problem
is the logarithm , which is computed by time stepping and extended to by time stepping backwards in time t.
1. Play with the code changing into with C a given number.
2. Show that by construction
Hint: Show that if , then (set and note that ) and . Conclude that , that is and so , choosing .
3. Show that log and exp are inverse functions (use that is the same as ).