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Re: Not getting answer to differential equation DSolve expression

• To: mathgroup at smc.vnet.net
• Subject: [mg38036] Re: [mg37989] Not getting answer to differential equation DSolve expression
• From: Vladimir Bondarenko <vvb at mail.strace.net>
• Date: Tue, 26 Nov 2002 00:50:26 -0500 (EST)
• In-reply-to: <200211250656.BAA14527@smc.vnet.net>
• References: <200211250656.BAA14527@smc.vnet.net>
• Reply-to: Vladimir Bondarenko <vvb at mail.strace.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Diana" <diana53xiii at earthlink.remove13.net> wrote on Monday, November 25, 2002, 2:56:03 AM :

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:  vvb at mail.strace.net
Voice:  (380)-652-447325 Mon-Fri 6 a.m. - 3 p.m. GMT
ICQ  :  173050619
Mail :  76 Zalesskaya Str, Simferopol, Crimea, Ukraine

• References:
  • Not getting answer to differential equation DSolve expression
    • From: "Diana" <diana53xiii@earthlink.remove13.net>