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JasonC1-Visitor
1-Visitor
January 10, 2017
Solved

How to enter differential equation?

  • January 10, 2017
  • 4 replies
  • 11123 views

How do I enter this differential equation into Mathcad 15, and make it find the symbolic result?

f'(x)=1+f(x)
solve for f(x)

( where f'(x) is the derivative of f(x) )

I know the answer is

f(x) =  e^x - 1


Thanks

Best answer by -MFra-

Hi Jason,

At each differential equation, you have to associate the initial conditions.

The simplest  method to solve the given type I first order ordinary differential equation, is the following:

Type 1 first order diff eq.jpg

4 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
January 10, 2017

    J
    JasonC1-VisitorAuthor
    1-Visitor
    January 10, 2017

    LOL yes I did use W.A., but I wanted to know how to enter it into Mathcad 

    -
    -MFra-21-Topaz IIAnswer
    21-Topaz II
    January 10, 2017

    Hi Jason,

    At each differential equation, you have to associate the initial conditions.

    The simplest  method to solve the given type I first order ordinary differential equation, is the following:

    Type 1 first order diff eq.jpg

      J
      JasonC1-VisitorAuthor
      1-Visitor
      January 10, 2017

      Thanks all.

      I've been a heavy user for many years, but embarrassingly, I've never used the below syntax, and don't know how to type in the circled part:

      circled.png

      Could someone nudge me in the right direction? What key stroke or mouse click? Which toolbar?

      TIA!

      -
      -MFra-21-Topaz II
      21-Topaz II
      January 10, 2017

      Hi Jason

      procedure 0.jpg

        L
        LucMeekes23-Emerald IV
        23-Emerald IV
        January 10, 2017

        Note that the solution to the DE you provide is not THE solution but A solution to that DE.

        Unfortunately Mathcad, nor Prime, provide a feature to solve for differential equations symbolically.

        F.M. shows a nice way of working around that, above.

        Then of course there is this method (A classical math problem: differential equations), which can be automated in Mathcad 11, but requires some hand work in later versions.

        Wit your specific example:

        Luc

          W
          Werner_E25-Diamond I
          25-Diamond I
          January 10, 2017

          You were already told that Mathcad can't solve differential equations symbolically automatically. You have to do it manually and Mathcad helps you with the integrals.

          But for the case of very simple ODEs of first order like yours, long time ago I once wrote a small routine (VdK) to solve them automatically (its for Mathcad 15 (and below)). Maybe you find it useful.

          VdK assumes that the independent variable is named x. There is also a routine Vdk2 in the attached file, which can deal with arbitrary variable names. As far as I remember that was the tricky part ,-)

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