       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

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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