Find the length of GH!
2 answers:
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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.
The way that you would do this is by taking 
out of the binomial, or as I like to think about it, 'un-distributing'. :p
out of 
, you end up with 
.
When you take out of 
, you get 
.
Put it together, and the solution is - 
.
Hope I helped!!
When you take
Put it together, and the solution is
Hope I helped!!