DSolve on 'simple' differential equations

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

Hi, 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. -- Space - The final frontier