Could you show the partial fractions of the expression
and then integration here ?
1. Solve
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.
The integral is written wrong. It should be:
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.
-Dan
For starters there is no way we can specify a solution of a first order ODE to pass through two arbitrary points. So the problem is automatically over-constrained from the start.
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).
-Dan
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).