In my studies, I encountered a question which I did not know how to do. The answer referred to implicit differentiation but I did not understand the steps undertaken, so could someone explain to me how to do the following question?
The answer states that . Where does the come from?, show that .
Then I had problem with Euler's method with the question:
How do I use Euler's method if all I have if ?Given that when , use Euler's method with a step-size of to estimate the value of when
lol, the solution is so simple now that I actually understand it Thank you.
Although I would have done it slightly differently (now that I understand what's going on):
As for Euler's method, it is question 4 e (section 2). from the 2006 VCE specialist math exam
So the problem is to solve y(0)= 2, using Euler's method with a step of 1/4, from 0 to 1/2. Did you expect us to guess that before?
Well, that's easy enough, you only have to do two steps! Since y(0)= 2, at 0, , at x= 0, is 2(1-2)= -2. The line with slope -2, starting at (0,2) is y= -2x+ 2 and at x= 1/4, y(1/4)= -2(1/4)+ 2= -1/2+ 2= 3/2.
Now do the same thing again. If y= 3/2, what is dy/dx= y(1- y)? What is the equation of the line through (1/4, 3/2) with that slope? What is y on that line when x= 1/2?