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DSolve on 'simple' differential equations

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  • Subject: [mg114505] DSolve on 'simple' differential equations
  • From: Oliver Jennrich <oliver.jennrich at>
  • Date: Sun, 5 Dec 2010 21:58:10 -0500 (EST)


I'm sure that I'm missing something obvious, but I try to get
Mathematica to solve the following differential equation:

deq = 2*Derivative[1][r][t]*Derivative[1][\[Phi]][t] +
r[t]*Derivative[2][\[Phi]][t] == 0

(or in short: 2 r' phi' + r phi'' = 0)

The solution is well known - multiply with r and find that the equation
is equivalent to

(r^2 phi')' = 0 

with the solution

r^2 phi' = const.

Mathematica sort of 'oversolves' the problem: I always get a solution of the form

{{\[Phi][t] -> C[2] + Integrate[C[1]/r[K[1]]^2, {K[1], 1, t}]}}

which is correct (of course) but misses the point.

DSolve[deq, \[Phi]'[t], t]

yields the same result as above (why?).

So is there a way to have Mathematica solve the diff.eq. in terms of
phi'? Of course, I can manually replace phi'-> u and phi''-> u', but
that is somewhat tedious.

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