## frank0520 one year ago Use separations of variables to solve the Differential Equation: K dN/dt = -r(N-K)(N-A) After doing partial fractions and the integration I get: (N-A)/(N-K) = C_1 e^((A-K)(-rt)/K) I am stuck solving for N

1. frank0520

$\frac{ N-A }{N-K }=C_1e^{\frac{ (A-K)(-rt) }{ K }}$ I am stuck in this part, solving for N

2. zepdrix

$\large\rm \frac{ N-A }{N-K }=c_1e^{stuff}$Multiply both sides by (N-K),$\large\rm N-A=(N-K)c_1 e^{stuff}$

3. zepdrix

Distribute,$\large\rm N-A=N c_1 e^{stuff}-K c_1 e^{stuff}$Let's subtract N to move it to the right side, and add Kc_1 e^(stuff) to the other side by adding,$\large\rm K c_1 e^{stuff}-A=N c_1 e^{stuff}-N$Then factor an N out of each term on the right side,$\large\rm K c_1 e^{stuff}-A=N (c_1 e^{stuff}-1)$And divide to isolate your N,$\large\rm \frac{K c_1 e^{stuff}-A}{c_1 e^{stuff}-1}=N$

4. zepdrix

If your K is just a constant, you can probably just absorb it into the c.$\large\rm \frac{c_2 e^{stuff}-A}{c_1 e^{stuff}-1}=N$

5. frank0520

Thanks for the help.

6. zepdrix

:D