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DSolve solution checking
*To*: mathgroup at christensen.cybernetics.net
*Subject*: [mg1011] DSolve solution checking
*From*: "Rich Klopp" <Rich_Klopp at qm.sri.com>
*Date*: Wed, 10 May 1995 02:35:17 -0400
I am having difficulties checking the solution of a 2nd order ODE obtained
using DSolve. I define the equation leftside == 0 using the next 3 lines:
r[z] := a z^2 + g
leftside = (r[z]^2 + e) D[u[z],{z,2}] +
D[r[z]^2,z] D[u[z],z];
bndEq = (leftside == 0)
4 a z (g + a z^2) u'[z] + (e + (g + a z^2)^2) u''[z] == 0
I then solve it for u[z] and get a huge output, (which, by the way, contains
DSolve`t... what does this mean?).
DSolve[bndEq, u[z],z] // Short
Sqrt[-Sqrt[<<1>>] + <<1>>] <<4>>
{{u[z] -> --------------------------------}}
2 2 4
Sqrt[e + g + <<1>> + a z ]
By obtaining a pure function solution, I should be able to back-substitute and
verify the answer.
DSolve[bndEq, u,z] // Simplify // Short
{{u -> Function[z, <<1>>]}}
Let's check the answer, which ought to equal zero upon substitution.
leftside /. % //Simplify //Short
{4 <<4>> + (e + <<1>>) <<1>>}
However, mathematica 2.2.1 on the PowerMac doesn't seem to know.
% == 0 //Short
{<<1>>} == 0
Why can't Mathematica tell if it got the right answer?
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