Getting the output of DSolve to look nicer

*To*: mathgroup at smc.vnet.net*Subject*: [mg129779] Getting the output of DSolve to look nicer*From*: mal359 at cornell.edu*Date*: Wed, 13 Feb 2013 04:48:51 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Is there any way to pass an option to DSolve or otherwise allow Mathematica to return the output of a DSolve command in an implicit or algebraically simple manner? There are a few differential equations where the solution given by Mathematica are absolutely horrible to look at, but they can be expressed so much more simply by leaving them in an implicit form. For example, the output from the command DSolve[y'[x] == 3x^2-2*x*y[x]+2+(6y[x]^2-x^2+3)*y'[x] = 0, y, x] is an explicit, three-part solution for y and is very, very nasty, whereas the solution can be expressed much more concisely with the equation x^3+2y[x]^3-x^2*y[x]+2x+3y[x] == C[1]. Is there any way to get the output of DSolve to look more like the nicer solution? Thanks for your help!