Math Forum / Math Software / Mathematica / October 2008

dodatki@poczta.fm schrieb:

Hi John,

try to replace y'[t] in the call to Sqrt by y'[x], and you'll get an exact
solution for p=2:
In[3]:= DSolve[{Sqrt[Derivative[1][y][x]^2 + 1] ==
    (x^(p - 1) + y[x]^(p - 1)*Derivative[1][y][
        x])/(x^p + y[x]^p)^(1 - 1/p),
   y[1] == 6} /. p -> 2, y, x]
Out[3]= {{y -> Function[{x}, 6*x]}}

Peter

=================^^^^^^
Must be y'[x] not of t.

In[1]:= sol[p_] :=
 NDSolve[{Sqrt[
     1 + (y'[x])^2] == (x^(p - 1) + (y[x])^(p - 1)*y'[x])/(x^p +
        y[x]^p)^(1 - 1/p), y[1] == 6}, y, {x, 1, 4}]

In[2]:= sol[2]

Out[2]= {{y->InterpolatingFunction[{{1.,4.}},<>]}}

In[3]:= Plot[y[x] /. %, {x, 1, 4}]

Regards,
-- Jean-Marc

You typed y[t] rather than y[x]

Bob Hanlon

---- dodatki@poczta.fm wrote:

=============
Hello!
Lately I wrote simple code in Mathematica

sol[p_] :=
 NDSolve[{Sqrt[
         1 + (y'[t])^2] == (x^(p - 1) + (y[x])^(p - 1)*y'[x])/(x^p +
               y[x]^p)^(1 - 1/p), y[1] == 6}, y, {x, 1, 4}]

but when I typed sol[2] the following kind of error was shown:

NDSolve::"ndnum": "Encountered non-numerical value for a derivative at
\
\!\(x\) == \!\(4.587812868332132`*^-296\)."

May I know what I'm doing wrong? Or how can I improve that code to
work correctly?
Thank you in advance
                                 John

--

Bob Hanlon

On Oct 5, 12:16 am, doda...@poczta.fm wrote:

x])/(x^p +

1, 4}]

John,

I think your error results from the fact that you have defined y as
both a function of x and as a function of t (y[t] and y[x]).  I am not
certain if you meant for y to be a function of both (in which case you
need to specify it as such (y[x,t]) throughout the equation (and
specify which derivatives you are taking) or if the y[t] on the left
side of your differential equation should be a y[x] (leaving you with
a tractable ordinary differential equation).  Hope that helps,

Marshall