The general solution of the differential equation $y''+\omega^2y=0$ can be written as: $$y=\alpha\cos{(\omega(t-c))}+\beta\sin{(\omega(t-c))}$$
Is it correct to say that:
- $\omega$ and $c$ are constants
- $\alpha$ and $\beta$ are arbitrary constants
- $t$ is a variable
QUESTION: What is the difference between constants, arbitrary constants and variables?
Best Answer
It is totally correct.
The solution of the equation, the function, depends on the value of t (called, the variable).
Also, the constants are properties of the system described by the differencial equation (the elasticity of a material or the mass of a pendulum, etc...), while the arbitrary constants give diferent solutions depending on the initial conditions of the system (for example, the initial phase of a mass connected to a spring).