Matlab for differential equations

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Discussion Overview

The discussion centers around the capabilities of MATLAB in solving differential equations, specifically whether it can provide analytical solutions or if it is primarily focused on numerical solutions. Participants explore the definitions of 'solving' in this context and compare MATLAB's functionalities with other software tools.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant asks if MATLAB can solve differential equations, prompting a clarification on whether 'solve' refers to analytical or numerical solutions.
  • Another participant provides an example of a differential equation and its general analytical solution, indicating that MATLAB's strength may lie more in numerical computation than in symbolic manipulation.
  • A different participant mentions that MATLAB includes a symbolic math toolbox, suggesting it can provide analytical solutions, but expresses uncertainty about its current capabilities and access to verify this.
  • There is a reference to MATLAB's historical use of Maple and MuPad for symbolic computations, indicating a potential evolution in its capabilities over time.

Areas of Agreement / Disagreement

Participants express differing views on MATLAB's ability to solve differential equations analytically versus numerically. There is no consensus on the extent of its capabilities, particularly regarding the symbolic math toolbox.

Contextual Notes

Some participants note limitations in their access to MATLAB's features, which may affect their ability to confirm claims about its functionalities.

Mathmanman
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Does MATLAB solve differential equations?
 
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Depends on what you mean by 'solve'. Are you talking analytically or numerically?
 
I mean like the general solution of a differential equation.
For example:
Solve xy'-4y = (x^6)(e^x)
General solution: y = x^5e^x – x^4e^x + cx^4
 
Mathmanman said:
I mean like the general solution of a differential equation.
For example:
Solve xy'-4y = (x^6)(e^x)
General solution: y = x^5e^x – x^4e^x + cx^4

This is called the 'analytical' solution. The 'numerical' solution obviously uses just numbers.

I think Matlab is more geared to numerical computation that symbolic manipulation.

For the latter, a package like Mathematica or Maple would have that capability.
 
I believe Matlab includes a symbolic math toolbox. It has been a long time, but I think that might have once been provided by an included subset of Maple, but I think they then switched to MuPad. This page seems to show that Matlab can give analytic solutions to differential equations via the toolbox and dsolve.

http://www.mathworks.com/help/symbolic/functionlist.html

I don't have access to that so I can't verify that it can solve your example.
 

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