Differential Equations

This worksheet illustrates how the solutions of a differential equation depend on parameters. The phase portrait below is that for the pendulum equation: \begin{align*} x' &= y\\ y' &= -a\sin x \end{align*} The red curves are a few trajectories. The blue curve is the the right hand side for the second equation. Use the slider to change the parameter \(a\).

Value of parameter \(a\):