2.0 A better way to understand Differential Equations | Nonlinear Dynamics | 2D Linear Diff Eqns

Part 1: https://youtu.be/ySfs8YVMY7Q Part 2: https://youtu.be/I9UEBRya4X0 Part 3: https://youtu.be/6mLCFyEv3Z0 These second-order linear differential equations can be written in the form dx/dt = ax + by dy/dt = cx + dy Depending on the values of a,b,c and d, the dynamics will be very different! They can be characterized by finding the eigenvalues and eigenvectors of the matrix A = [a, b; c, d]. This is a necessary first step to getting qualitative pictures about nonlinear 2nd order differential equations - something we'll talk about in part 3. Chapters: 0:00 Intro & Recap 0:27 Spring Mass Damper Equation of Motion 1:25 Spring Mass Damper Vector Field 2:28 Spring Mass Damper State Space form 2:58 General Solution to Linear System 5:17 Saddle Example 7:02 Characterization of Linear Systems from Eigenvalues 8:23 Summary Animations & Outro Music: Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u Other Music: Nuclear Lynx - Discovery