Re: Simple DSolve equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg122640] Re: Simple DSolve equation*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 4 Nov 2011 06:00:47 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111030846.DAA15245@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

a) The solution given is correct, and b) You gave no restrictions on k. Nor did you ask for any, in Mathematica. Here's a possible way to go about it: Clear[y, k, m] y = y /. First@DSolve[{y''[x] == k y[x], y[0] == 0, y'[0] == m}, y, x] Function[{x}, (E^(-Sqrt[k] x) (-1 + E^(2 Sqrt[k] x)) m)/(2 Sqrt[k])] s1 = Quiet@Solve[y[10] == 0, {m, k}] y[10] /. s1 Length@% {{k -> -\[Pi]^2}, {k -> -((81 \[Pi]^2)/100)}, {k -> -((16 \[Pi]^2)/ 25)}, {k -> -((49 \[Pi]^2)/100)}, {k -> -((9 \[Pi]^2)/ 25)}, {k -> -(\[Pi]^2/4)}, {k -> -((4 \[Pi]^2)/25)}, {k -> -(( 9 \[Pi]^2)/100)}, {k -> -(\[Pi]^2/25)}, {k -> -(\[Pi]^2/ 100)}, {k -> Log[-(-1)^(1/10)]^2}, {k -> Log[-(-1)^(1/5)]^2}, {k -> Log[-(-1)^(3/10)]^2}, {k -> Log[-(-1)^(2/5)]^2}, {k -> Log[-(-1)^(3/5)]^2}, {k -> Log[-(-1)^(7/10)]^2}, {k -> Log[-(-1)^(4/5)]^2}, {k -> Log[-(-1)^(9/10)]^2}, {m -> 0}} {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} 19 This indicates 18 k values that work for any m, and one m value that works for any k. The suppressed error message (remove Quiet) indicates OTHER solutions may exist, but I think not. Bobby On Thu, 03 Nov 2011 03:46:30 -0500, Rui <rui.rojo at gmail.com> wrote: > Why does something like this not give the correct answer with > restrictions over k? > How would you go about getting the right general solutions in these kind > of basic differential equations? > > Thanks > > DSolve[{y''[x] == k y[x], y[0] == 0, y[10] == 0}, y[x], x] > Out={{y[x] -> 0}} > -- DrMajorBob at yahoo.com

**References**:**Simple DSolve equation***From:*Rui <rui.rojo@gmail.com>