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Differential equation boundary conditions

  • Thread starter kasse
  • Start date
  • #1
366
0
[tex]
\frac{dN}{dt}=-k_sN^2
[/tex]

Attempt:

[tex]
\frac{1}{N^2}dN = -k_s dt
[/tex]

Integrate:

[tex]
-\frac{1}{N} + C = -k_s t
[/tex]

In the solution manual, C is written [tex]\frac{1}{N_0}[/tex]

Why?
 
Last edited:

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18
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
Cyosis
Homework Helper
1,495
0
Alternatively use the boundary conditions in this case [itex]N(0)=N_0[/itex] and then solve for C.
 

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