# Differential equation boundary conditions

1. May 3, 2009

### kasse

$$\frac{dN}{dt}=-k_sN^2$$

Attempt:

$$\frac{1}{N^2}dN = -k_s dt$$

Integrate:

$$-\frac{1}{N} + C = -k_s t$$

In the solution manual, C is written $$\frac{1}{N_0}$$

Why?

Last edited: May 3, 2009
2. May 3, 2009

### dx

If you integrate from 0 to t on the right, you have to integrate from N0 to Nt on the left, where N0 is the value of N at t = 0.

3. May 3, 2009

### Cyosis

Alternatively use the boundary conditions in this case $N(0)=N_0$ and then solve for C.