Re: DSolve and N do not commute

*To*: mathgroup at smc.vnet.net*Subject*: [mg40213] Re: [mg40184] DSolve and N do not commute*From*: Dr Bob <drbob at bigfoot.com>*Date*: Wed, 26 Mar 2003 02:42:02 -0500 (EST)*References*: <200303250804.DAA08372@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

It's a bug. Here's the general solution: general = a f'[r] + f''[r] == b f[r]; s0 = f /. First@DSolve[general, f, r] /. C -> A general /. f -> s0 // Simplify Function[{r}, E^((1/2)*(-a - Sqrt[ a^2 + 4*b])*r)*A[1] + E^((1/2)*(-a + Sqrt[ a^2 + 4*b])*r)*A[2]] True And here's the solution with those constants, with N before DSolve. constants = {a -> (8/3)*2^(2/3), b -> (-(8/3))*2^(1/3)}; eq2 = N[general /. constants]; s2 = f /. First@DSolve[eq2, f, r] Function[{r}, C[1]/E^(3.174802103936397* r) + (r*C[2])/ E^(3.174802103936397*r)] Here's a simple check for correctness: eq2 /. {f -> s2} // Simplify (-2.116534735957597*C[2])/ E^(3.174802103936397*r) == 0 and that is zero only if C[2]==0. (How about that?) eq2 //. {f -> s2, C[2] -> 0} // Simplify True Here's another check, going back to the general equation: general /. Flatten@{f -> s2, constants} // Simplify; Chop@% (-2.1165347359575954*C[2])/E^(3.174802103936397*r) == 0 Again, setting C[2] to zero gives a correct solution. s2[r] /. C[2] -> 0 C[1]/E^(3.174802103936397*r) But if C[2] isn't zero, the solution is wrong, and that's a BUG. Bobby On Tue, 25 Mar 2003 03:04:52 -0500 (EST), arkadas ozakin <arkadaso at hotmail.com> wrote: > Take the following differential equation, > > eq = (f''[r] + 8 2^(2/3)/3 f'[r] == -8 2^(1/3)/3 f[r]) > > DSolve[eq, f[r], r] gives something like > > f[r] -> C[1] Exp[k1 r] + C[2] Exp[k2 r] > > where k1 and k2 are two different numbers. > > However, > > DSolve[N[eq],f[r],r] gives something like > > f[r] -> (C[1] + C[2] r) Exp[k2num r] > > where k2num is the numerical version of the constant k2 above. > > I don't know how DSolve handles numerical constants, but the > discrepancy between the two results wasn't something I expected > (that's why it took me quite a bit of time to figure out what was > going wrong in my longish Mathematica notebook...) > > Does anyone know why this happened? Is this a bug, or am I doing > something wrong? Any suggestions for avoiding similar things in the > future? > > arkadas > > -- majort at cox-internet.com Bobby R. Treat

**References**:**DSolve and N do not commute***From:*arkadaso@hotmail.com (arkadas ozakin)