Answer:
Computation.
Step-by-step explanation:
I'm not really sure if that's the analytical solution of the inital value problem,
because y(0)=11-ln(1-0)(3)=11. Howevwer, let us procede with the given values...
Let us assume that we are going to use euler with n=2 (two steps) and h=0.2(the size of each step)
The update rules of the Euler Methode are
Since the initial value problem tells us that Y=1 when X=0, we know that
and that
. Then, we have
and
which gives us the points (0,1), (0.2, 5.2) and (0.4, 27.12).
Now, since we want to compare the analyticaland the Euler result, we first compute the value of y=11-ln(1-x)(3) for the values x=0, 0.2 and 0.4. We get that
and we compute for each i.
It holds
which tells us that we have a really bad approximation, as I already stated there must be a mistake in the analytical solution since the intial values don't coincide. Also note that the curve that we get using the euler methose is growing faster than the analitical solution.