How to | Plot the Results of NDSolve - Wolfram
NDSolve solves a differential equation numerically. It returns solutions in a form that can be readily used in many different ways. One typical use would be to produce a plot of the solution. As an example, take the equation with the initial conditions and :
plotting - How do I plot a solution of a differential equation ...
I believe the main issue for you is that Mathematica does not know what x[t] and y[t] are in your ParametricPlot command. An excellent way to solve this is by using ReplaceAll (a.k.a. /. ) with the Rule s already included in the solution produced by DSolve .
How can I plot the direction field for a differential equation?
2015年7月17日 · For a first sketch of the direction field you might use StreamPlot: Axes -> True, AspectRatio -> 1/GoldenRatio] No need to solve the differential equation to generate a direction field. According to the Wikipedia lemma on slope fields you can plot the vector {1, (y + Exp[x])/(x + Exp[y])}: or perhaps you could use a stream plot:
DSolve: Solve a Differential Equation—Wolfram Documentation
DSolve can solve ordinary differential equations (ODEs), partial differential equations (PDEs), differential algebraic equations (DAEs), delay differential equations (DDEs), integral equations, integro-differential equations, and hybrid differential equations.
Let's use some syntax to clean things up in order to define the solution to a function which we can plot, find its derivative, etc. Define the function xsol[t] which will be this analytic solution to the DE.
plotting - Plot the solution of a differential equation - Mathematica …
2024年5月23日 · Differential equation $\frac{\partial e}{\partial w}=\frac{e}{w}$ can be integrated in general form as $w=c e$, where c is arbitrary constant. The global minimum is defined in a form
MATHEMATICA tutorial, Part 1.1: Plotting Solutions to ODEs
2024年12月23日 · In this command, I am plotting a family of solutions to a differential equation. This command is not really any different from a normal plot command. The primary difference is that I have created a list of samples in a table. These samples have the variable c and then I can plug in different values of c to create the values in this table.
MATHEMATICA TUTORIAL, Part 1.2: Plotting Solutions - Brown …
In this command, you define the differential equation that you want to solve and the initial conditions (the respective x and y values). Flattening creates a list of the equations. Then you are asking Mathematica to evaluate the different equations according to …
The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathe-matica function NDSolve, on the other hand, is a general numerical differential equation solver.) DSolve can handle the following types of equations: † Ordinary Differential Equations (ODEs), in which there is a single independent variable t and
MATHEMATICA tutorial for Applied Differential Equations I
2024年12月24日 · Mathematica provides friendly tools to solve and plot solutions to differential equations, but it is certainly not a panacea of all problems. This computer algebra system has tremendous plotting capabilities. There is a free version of Mathematica featuring its syntax and functions--- Mathics that was developed by a team led by Jan Pöschko.
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