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Practice Problems

Phase Portrait Generator

Phase Portrait Generator

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Sketch the phase plane portrait of a 2D system of first order differential equations. The vector field is made up of vectors in the direction of dy/dx at individual points (x,y). Tracing a path of vectors yields a solution to the ordinary differential equation at a set of initial conditions. Initial value curves can be plotted by inputting initial (x,y) values or by clicking anywhere on the portrait.

This plotter utilizes the Runge-Kutta method in order to plot solutions. As such, some systems (particularly those with very large derivatives) may generate ugly looking plots. Adjusting the smoothness may help correct these errors, although smoother plots will take longer to generate. Additionally, overly-steep systems can be corrected by enabling steep correction which will extrapolate solutions only up to a certain increment per step. Note, however, that steep correction will decrease the length of the solution curve and may distort some functions. Some functions, though, will inevitably produce errors when plotted.