Not getting answer to differential equation DSolve expression
Diana
What does it mean when I submit a differential equation, and the same
equation appears as the output?
I have tried this equation:
DSolve[y'[x] == (-x^2 + 2 y[x]^(-3))/(2 x y[x] - 3 x^2), y[x], x]
Is it too complicated for the program?
Diana
Tom Burton
<diana...@earthlink.remove13.net> wrote:
Yes, in general, if Mathematica returns input unprocessed without comment,
you may conclude that Mathematica cannot process it, for whatever reason.
(Sometimes Mathematica is not sure why, so better to say nothing. In this
case, perhaps a hint would be nice.) This differential equation, though not
"complicated", is strongly nonlinear. Few such DE's admit analytical
solutions. Try NDSolve.
Tom Burton
Vladimir Bondarenko
D> What does it mean when I submit a differential equation, and the same
D> equation appears as the output?
Mathematica cannot find the answer.
D> I have tried this equation:
D> DSolve[y'[x] == (-x^2 + 2 y[x]^(-3))/(2 x y[x] - 3 x^2), y[x], x]
D> Is it too complicated for the program?
In the version you tried, yes.
Please note that y'[x] = dy/dx = 1/(dx/dy)= 1/x'[y]
(This trick only works with the first derivative, don't jump to a conclusion
that y''[x] = 1/x''[y], that's totally wrong - by the way, why? ;-)
(* DSolve[y'[x] == (-x^2 + 2 y[x]^(-3))/(2 x y[x] - 3 x^2),y[x], x] *)
In[1] := DSolve[x'[y] == (-x[y]^2 + 2 y^(-3))/(2 x[y] y - 3 x[y]^2), x[y], y]
Out[1] = {{x[y] -> y/3 - (2^(1/3)*y^4)/(3*(-27*y^4 - 2*y^9 + 27*y^6*C[1] +
Sqrt[-4*y^18 + (-27*y^4 - 2*y^9 + 27*y^6*C[1])^2])^(1/3)) -
(-27*y^4 - 2*y^9 + 27*y^6*C[1] + Sqrt[-4*y^18 + (-27*y^4 - 2*y^9 +
27*y^6*C[1])^2])^(1/3)/(3*2^(1/3)*y^2)}, {x[y] -> y/3 + ((1 +
I*Sqrt[3])*y^4)/(3*2^(2/3)*(-27*y^4 - 2*y^9 + 27*y^6*C[1] +
Sqrt[-4*y^18 + (-27*y^4 - 2*y^9 + 27*y^6*C[1])^2])^(1/3)) +
((1 - I*Sqrt[3])*(-27*y^4 - 2*y^9 + 27*y^6*C[1] + Sqrt[-4*y^18 +
(-27*y^4 - 2*y^9 + 27*y^6*C[1])^2])^(1/3))/(6*2^(1/3)*y^2)},
{x[y] -> y/3 + ((1 - I*Sqrt[3])*y^4)/(3*2^(2/3)*(-27*y^4 - 2*y^9 +
27*y^6*C[1] + Sqrt[-4*y^18 + (-27*y^4 - 2*y^9 + 27*y^6*C[1])^2])^(1/3)) +
((1 + I*Sqrt[3])*(-27*y^4 - 2*y^9 + 27*y^6*C[1] + Sqrt[-4*y^18 +
(-27*y^4 - 2*y^9 + 27*y^6*C[1])^2])^(1/3))/(6*2^(1/3)*y^2)}}
That is you have 3 implicit equations connecting x and y. Your ODE is solved.
Best wishes,
Vladimir Bondarenko
Mathematical and Production Director
Symbolic Testing Group
Email: v...@mail.strace.net
Voice: (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
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Mail : 76 Zalesskaya Str, Simferopol, Crimea, Ukraine
Stan
Try using NDSolve and put in some BCs, it may not be solvable
analytically, but should be solvable numerically.
Kevin J. McCann
all that.
Kevin
"Stan" <sna...@runbox.com> wrote in message
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