MATH 215/255
Fall 2014
Comments about Homework 1
1) In question 1.2.103, many students stated that the function was undefined at x = 1.
Nobody gave a more precise statement about it. It would have been good to see them
mention Picard’s theorem and why they checked whether f (x, y) was defined at x = 1
specifically.
2) In question 1.1.6, they integrated both sides with respect to x and said the integral
(y 2 −1)dx = (1/3)y 3 −y+c. The majority of students however did the partial fractions
correctly or else used that the integral was arctanh(x). One student mistakenly said
arctan(x).
3) The most common problem was in choosing what |x−1| or |y(x)−1| is supposed to be.
Nobody said anything about the initial conditions when choosing whether it is equal
to x − 1 or 1 − x. Most people left answer in implicit form (e.g. t2 = ln|x − 1|/|x + 1|).
However some students tried to solve for x (as in e.g. above) and would do so choosing
the wrong sign. This resulted in a wrong final answer.
4) For question 1.2.3. several students did not label the axis, made too few slope lines,
or were very messy in their drawings.