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[MUG] Re: dsolve does not find second solution
| [MUG] Re: dsolve does not find second solution |
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Author: Zijlstra
Posted: Thu, 19 Dec 2002 09:41:15 -0600
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>> From: zijlstra "zijlstra"
Dear Dr. Kahovec,
The solutions are indeed (explicit) branches of one (implicit) solution. MAPLE
should return either both (explicit) branches or stop at the implicit
solution. The reason it omits one branch is in the method of solution: rather
than realizing that the problem is exact (which makes for a very
straightforward dtermination of the implicit solution), MAPLE
first arrives at the type homogeneousD. Solutions of this type are generated
in 'RootOf' form. But MAPLE does not stop there. Rather, it returns an
closed form solution using 'allvalues' - the probable source of omission of
the second branch.
The bigger problem here is: why does MAPLE not recognize this ODE as exact?
>ode1:=diff(y(x),x)=-(4*x+3*y(x)+1)/(3*x+2*y(x)+1);
>with(DEtools):
>odeadvisor(ode1,y(x),[exact]);
[NONE]
Hope this narrows down the problem some,
Jan Zijlstra, Dept. Math. Sci., MTSU
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