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?