Re: DSolve problem

• To: mathgroup at smc.vnet.net
• Subject: [mg60105] Re: DSolve problem
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 2 Sep 2005 06:37:39 -0400 (EDT)
• Organization: The Open University, Milton Keynes, U.K.
• References: <df946n\$62v\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```sunnewton wrote:
> Hi,
> I am a freshman of Mathematica, I need help here...
>
> I met such problem as:
>
> DSolve[y'[x] == sin[t] - 2y[x], y[x], t]
>
> DSolve::"dvnoarg": "The function \!\(y[x]\) appears with no arguments."
>
> How to Handle???
>
First, correct the syntax error: sin[t] must be written Sin[t] with a
capital "S" (Any built-in Mathematica functions starts with a capital
letter).

Second, answer the following question: Is the function y depends on the
variable x or t? Depending on your answer to this question and assuming
that the ODE itself is correctly written, you can write either of the
following DSolve commands:

In[1]:=
DSolve[Derivative[1][y][x] == Sin[t] - 2*y[x], y[x], x]

Out[1]=
{{y[x] -> C[1]/E^(2*x) + Sin[t]/2}}

In[2]:=
DSolve[Derivative[1][y][t] == Sin[t] - 2*y[t], y[t], t]

Out[2]=
{{y[t] -> C[1]/E^(2*t) + (1/5)*(-Cos[t] + 2*Sin[t])}}

The third argument of *DSolve* is the variable(s) used to solve the ODE.
The second argument is the function(s) to which you want a solution:
here, you have the choice to ask for a solution expressed as pure
function, if you set the argument to y only, or as an expression with
the variable, if you set the argument to y[x] or y[t]. Whatever your
choice is, however, you still have to list explicitly the variable as
third argument.

Hope this helps,
/J.M.

```

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