Re: Surprising DSolve problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg123999] Re: Surprising DSolve problem*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Wed, 4 Jan 2012 05:05:55 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201201020742.CAA09063@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

That works: Clear[y] y[x_] = y[x/a] /. First@DSolve[y''[x] + (2 y[x])/(Cosh[x]^2) == 0, y, x] // FullSimplify y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) // Simplify -C[2] + (C[1] + ArcTanh[Tanh[x/a]] C[2]) Tanh[x/a] 0 Bobby On Tue, 03 Jan 2012 04:29:47 -0600, Dave Snead <dsnead6 at charter.net> wrote: > Sam, > > Mathematica is deficient in this area. > (Hopefully they'll improve this someday) > > Use it to solve > y''[x] + (2 y[x])/(Cosh[x]^2) == 0 > for y and then substitute x->x/a for a solution to > y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) == 0 > > Cheers, > Dave Snead > > > -----Original Message----- > From: Sam Takoy > Sent: Sunday, January 01, 2012 11:42 PM > To: mathgroup at smc.vnet.net > Subject: Surprising DSolve problem > > Hi, > > I find that my Mathematica (8.0.1) > > can do > > DSolve[ y''[x] + (2 y[x])/(Cosh[x]^2) == 0, y, x] > > but can't do > > DSolve[ y''[x] + (2 y[x])/(a^2 Cosh[x/a]^2) == 0, y, x] (*Additional > constant "a") > > If I am not mistaken, the equations are equivalent by a trivial change > of variables. > > What's going on here? > > Thanks, > > Sam > > > -- DrMajorBob at yahoo.com

**References**:**Surprising DSolve problem***From:*Sam Takoy <sam.takoy@yahoo.com>