1. Solve

$\displaystyle dP/dt = P(a-bP)$ where a and b are constants

$\displaystyle dP/[P(a-bP)] = dt$

rewrote the integral as

$\displaystyle -dP/[P(bP-a)] = dt$

then used this list of integrals [HTML]http://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions[/HTML]

$\displaystyle 1/a[ln((bP-a)/P)] = t + C$

multiply both sides by a and raise everything to e

$\displaystyle (bP-a)/P = Ce^a^t$

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)

$\displaystyle x dy/dx = y^2 - y$

$\displaystyle 1/ (y^2 - y) = 1/x dx$

used partial fractions on left side to get

$\displaystyle [-1/y + 1/(y-1)] dy = 1/x dx$

$\displaystyle -ln y + ln(y - 1) = ln x + C$

$\displaystyle ln[(y-1)/y] = ln x + C$

$\displaystyle (y-1)/y = Cx$

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.