Could you show the partial fractions of the expression
and then integration here ?
where a and b are constants
rewrote the integral as
then used this list of integrals [HTML]http://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions[/HTML]
multiply both sides by a and raise everything to e
I'd appreciate it if someone could check this for me and tell me what I might have done wrong.
2. Find a solution that passes through the points (0, 0) and (0, 1)
used partial fractions on left side to get
I'm pretty sure I did something wrong, most likely with the partial fractions b/c if you put the given points into my answer it yields 0=0 and DNE so I'd appreciate if someone could tell me what I did wrong.
Thanks in advance.
Also, you are raising the arbitrary constant to the e-th power, which is fine. However you have left it as an arbitrary constant in your final answer. (ie. you are calling it "C.") Please note that this new C you are talking about can never be negative, so it is not quite an arbitrary constant. I would suggest stating your solution and adding the comment that C > 0.
I did this problem as a Bernoulli equation and got a different solution.
I did it your way and got your solution. I am not certain why the two forms do not match up. Anyway, my solution can be passed through the point (0, 1), but not (0, 0).
Wait. They do match up, but they aren't quite in the same form. Both forms can pass through (0, 1), but not (0, 0).