Autonomous First Order Differential Equations

Instagram: https://www.instagram.com/engineering_made_possible/ Autonomous Differential Equation Problems (0:00) (0:27) – Problem statement: Consider the autonomous first-order differential equation dy/dx=y-y^3 and the initial condition y(0)=y0. By hand, sketch the graph of a typical solution y(x) when y0 has the given values. (4:06 & 7:32) – Problem statement: In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order differential equation. Classify each critical point as asymptotically stable, unstable, or semi-stable. By hand, sketch typical solution curves in the regions in the xy-plane determined by the graphs of the equilibrium solutions.