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MathGroup Archive 2005

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Re: DSolve doesn't solve easy dif. equation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56097] Re: [mg56045] DSolve doesn't solve easy dif. equation?
  • From: Devendra Kapadia <dkapadia at wolfram.com>
  • Date: Fri, 15 Apr 2005 04:47:45 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On Thu, 14 Apr 2005, Severin Posta wrote:

> Hi,
> when I try to solve
> 
> DSolve[(-(64 + 302*z + 744*z^2 + 1389*z^3 + 2043*z^4 + 1887*z^5 + 
> 1161*z^6 + 624*z^7 + 366*z^8 + 140*z^9 + 28*z^10))*
> f11[z] + 9*z*(-2 - 5*z + 5*z^3 + 2*z^4)*(-2 - 10*z - 3*z^2 + 20*z^3 + 
> 25*z^4 + 18*z^5 + 6*z^6)*Derivative[1][f11][z] +
> 9*z^2*(-2 - 5*z + 5*z^3 + 2*z^4)*(-2 - 7*z - 7*z^2 + 7*z^4 + 7*z^5 + 
> 2*z^6)*Derivative[2][f11][z] == 0, f11[z], z]
> 
> I get many strange looking messages..?
> 
> Why?
> 
> 
> 
> Thanx!
> 
> Sever.
> 
Hello Severin,

Thank you for reporting the problem with error messages and bad output
in the above DSolve example.

The error messages arise while attempting to solve the given second
order linear ODE using Kovacic's algorithm. Specifically, they arise
due to incorrect handling of the imaginary roots of a certain polynomial
during the calculation.

One solution of this ODE is the function f11[z] given below:

================================================================
In[1]:= $Version

Out[1]= 5.1 for Linux (February 20, 2005)

In[2]:= eqn = (-(64+302*z+744*z^2+1389*z^3+2043*z^4+1887*z^5+
              1161*z^6+624*z^7+366*z^8+140*z^9+28*z^10))*
              f11[z]+9*z*(-2-5*z+5*z^3+2*z^4)*(-2-10*z-3*z^2+
              20*z^3+25*z^4+18*z^5+6*z^6)*Derivative[1][f11][z]+
              9*z^2*(-2-5*z+5*z^3+2*z^4)*(-2-7*z-7*z^2+7*z^4+
              7*z^5 + 2*z^6)*Derivative[2][f11][z];

In[3]:= f11[z_] = ((1 + 2*z)*(-2 + z + z^2))/(z^(4/3)*(1 + z)^(4/3));

In[4]:= FullSimplify[eqn]

Out[4]= 0

====================================================================

A second linearly independent solution can also be computed using a
(non-trivial) symbolic integration.

Sorry for any inconvenience caused by this problem.

Sincerely,

Devendra Kapadia,
Wolfram Research, Inc.





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