Re: Change of function in an ODE

*To*: mathgroup at smc.vnet.net*Subject*: [mg109053] Re: Change of function in an ODE*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Mon, 12 Apr 2010 06:51:44 -0400 (EDT)

eqn = Module[{R}, R[r_] = r^2 Log[r] g[r]; r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] - L^4 r^4 R[r] == 0] // Simplify r (L^4 r^3 g[r] Log[r]-3 (8+3 Log[r]) (g^\[Prime])[r]-r ((24+23 Log[r]) (g^\[Prime]\[Prime])[r]+r (2 (2+5 Log[r]) (g^(3))[r]+r Log[r] (g^(4))[r])))==0 You still need initial conditions, and you can probably omit the factor r... since the expression won't be useful near r == 0, due to the Log[r] terms. Bobby On Sun, 11 Apr 2010 03:32:53 -0500, Sam Takoy <sam.takoy at yahoo.com> wrote: > Hi, > > I'm solving > DSolve[r^4 R''''[r] + 2 r^3 R'''[r] - r^2 R''[r] + r R'[r] - > L^4 r^4 R[r] == 0, R[r], r] // Simplify > > Now, I would like to make the substitution R[r]=r^2 Log[r] G[r], > formulate the equation for G[r] and solve it. What's the proper syntax > for that? > > Thanks, > > Sam > -- DrMajorBob at yahoo.com