Why Is C Written as \frac{1}{N_0} in the Solution Manual?

Thread starter kasse
Start date May 3, 2009
Tags

Differential Differential equation

In summary, a differential equation is a mathematical equation that relates a function to its derivatives and is used to model physical systems. The two main types are ordinary differential equations (ODEs) and partial differential equations (PDEs), and they are used in various fields such as physics, engineering, and biology. Differential equations can be solved analytically or numerically, and initial and boundary conditions help determine the specific solution.

May 3, 2009

kasse

[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?

Physics news on Phys.org

May 3, 2009

Homework Helper

Gold Member

You posted this already and I replied to it in the other thread.

FAQ: Why Is C Written as \frac{1}{N_0} in the Solution Manual?

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to model and analyze physical systems.

What are the types of differential equations?

The two main types of differential equations are ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve a single independent variable, while PDEs involve multiple independent variables.

What are some applications of differential equations?

Differential equations are used in many fields, such as physics, engineering, economics, and biology. They can be used to model and predict the behavior of systems in these fields, such as the motion of a falling object or the growth of a population.

How are differential equations solved?

Differential equations can be solved analytically or numerically. Analytical solutions involve finding an exact, closed-form solution using mathematical techniques. Numerical solutions use algorithms and computer programs to approximate the solution.

What are initial and boundary conditions in differential equations?

Initial conditions are values given at a starting point that are used to solve a differential equation, while boundary conditions are values given at the boundaries of the system. These conditions help determine the specific solution to the differential equation.