Using Mathematica for ODEs, Part 3 (DSolve, VectorPlot...make a Slope Field for an Autonomous Eqn)

(0:00) Introduction
(0:46) Example
(1:56) General solution of dy/dt=3y
(2:53) Define y[t_]:=c*E^(3t) in Mathematica and check that it works
(3:51) Clear[y] and use DSolve
(4:39) Solve the IVP by hand and with DSolve
(5:46) Use Show, VectorPlot, and Plot to graph the solution in the slope field.
(8:18) Interpret the slope field for this autonomous differential equation. It's constant in slope along horizontal lines. Horizontal translations of solutions are solutions.
(10:06) Equilibrium solution at y = 0

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[johnsinclair]

Excellent ODE video series in Mathematica. Very helpful, thanks!

[IndigoSolace]

How do I enter in a PDE into the VectorPlot? I'm having trouble with the syntax.


i.e


PDE = D[V[x, y], x, x] + D[V[x, y], y, y];
f[y] = PDE;


Show[VectorPlot [{1, f[y]}, [{x, -0.01, 0.11}, {y, -0.005, 0.053},
PlotPoints -> 50, ColorFunction -> "BlueGreenYellow",
Contours -> 10, ContourStyle -> White, Frame -> True,
FrameLabel -> {"x", "y"}, ClippingStyle -> Automatic,
Axes -> True, AxesLabel -> {"Length (m)", "Width (m)"},
PlotLabel ->
Style["Electric Field Intensity when p_v = 0"] StreamStyle ->
Black]]]


The command gets executed, but no plot appears. I tried to apply some of what you did here, but nothing changed for me.

[Mrsbhuiyan]

Thanks for these videos. Is it possible to use VectorPlot for a system of ODEs?

[siddharthkawadiya]

How do you plot vector field instead of the slope field?