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/5^1/2

• 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 2^1/2

Now practice with Mathematica

Advanced Examples