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Mechanics
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T. Tsujioka
Advanced Seminar
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Mechanics

0. Mathematical Preliminaries

2. Differential Equations
2-1. Separation of variables

__There are many methods developed for solving differential equations. Here, we only describe convenient method by
Separating variables. First, check the first degree differential equations.

Illustrated Example 2-1. Solve the following differential equations.

Explanations and Answers: 2-1.

__The first order differential equation of type:

,where a0.
If F(t) = 0, this type appears as exponential decay in many physical phenomena, such as the cooling of a hot object's temperature,
the some types of chemical reactions, the decay of radioactive substance, etc. If F(t) = constant, the solution is obtained to be
x(t) = Ae-t/a+ B, where A, B are constant. In general case, F(t)const., and even a, b may be a function, the method of variation of constants described in the next section can be utilized, or numerical method may be adopted to plot the variations in x(t).

 

 

 

 

 

 

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