Re: How to prevent Solve from DSolve?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg908] Re: How to prevent Solve from DSolve?
• From: bronstei at inf.ethz.ch (Manuel Bronstein)
• Date: Sun, 30 Apr 1995 03:42:35 -0400
• Organization: Dept. Informatik, Swiss Federal Institute of Technology

```In article <3nkbu2\$mq8 at news0.cybernetics.net>,
Richard Q. Chen <chen at fractal.eng.yale.edu> wrote:
>Hi,
>	I find it very frustrating that Mma always tries
>to give explicit solutions to an ODE, even if the solutions are
>so complicated as to be useless. For example
>
>In[2]:= Needs["Calculus`DSolve`"]
>
>In[3]:= DSolve[2 y[x] + (x + y[x]) y'[x] == 0, y[x], x]
>
>Out[3]= {{y[x] ->
>
> [... large output deleted ...]
>
>I would like to have Mma out put something like f(x,y) == C[1] so
>that I will know what kind of simpler function f(x,y) may be. I can
>then choose to solve for y in terms of x if it is desirable.
>

You're right, that's the proper way to return solutions of nonlinear odes.
FYI, if you have access to a copy of Axiom, that's exactly the kind of
answer it's returning on such problems (the '== C[1]' is not printed, but
that's the meaning of the output):
(1) ->y := operator y

(1)  y
Type: BasicOperator
(2) ->solve(2 * y x + (x + y x) * D(y x,x) = 0, y, x)

2
2y(x)  + 6x y(x)
(2)  ----------------
+----+
3\|y(x)
Type: Union(Expression Integer,...)

Interestingly, not as simple a first integral as the one you got by hand.

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Fax: [+41] (1) 632-1172

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```

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