Interactive Dynamical Features in Differential Equations - Advanced Examples
Often we are interested in studying how certain characteristics of solutions depend on initial conditions and parameters.
Among others, typical examples include:
- Limiting behavior of zeroes
y''[t] + 2 y'[t] + 6 y[t] == 0, y[0] == 2, y'[0] == a
As a → infinity, first positive zero → Pi/51/2
- Existence of extrema
2 y''[t] + 3 y'[t] - 2 y[t] == 0, y[0] == 1, y'[0] == -b
b=1 b=2
- Critical values of damping coefficients
Critical damping = 2 (k m)1/2 = 8 21/2
Now practice with Mathematica