Question

I found the approximation for Euler Implicit and explicit methods for the following equations:
dy/dx = (x+y-1)2
with initial value
y(0) = 2;
step size (h) = 0.1
and x = 0 to 1.5.
They are asking me to compared the approximated values with the exact answer of the equation at these points. How do I find the exact values??? I tried using Bernoulli's eq. but it didn't work.

Answer 1

should that read to the power 2?

Answer 2

yes

Answer 3

Looking at this quickly there does not appear to be a quick solution although one may be available, possibly the best way forward until you can see a quicker route is to use intgrating factors. A good example of how this method works this is seen in Paul's online differential equations notes. Unfortunately this is a long process but you will get the right answer if you follow the algorithm strictly.

Answer 4

is there a quicker way of getting the exact answer since the purpose of my problem was to use the euler's implicit and explicit methods, the exact answer is just needed to get the error

Answer 5

the actual answer to \[ dy/dx=(x+y-1)^{2}\] is very complicated and actually involves complex exponents so you may want to check your question, alternatively try an internet based derivative calculator such as wolframalpha

Answer 6

I was trying to use matlab but I don't know how to input it correctly and it gives me errors...

Thanks for your help! ;)

Answer 7

you're welcome, I can't use matlab either ;) good luck

Answer 8

thanks! In that website you gave me they gave me y solved as
y = (1 / (c*e^2ix - i/2) ) - x + (1 - i)

What is the i ?

Answer 9

Just a guess, but i may be the imaginary operator "i" that is equal to\[\sqrt{-1}\]

Answer 10

ok, thank you!