# Differential equation boundary conditions

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

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?

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