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Re: Simple DSolve equation

• To: mathgroup at smc.vnet.net
• Subject: [mg122628] Re: Simple DSolve equation
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 4 Nov 2011 05:58:37 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201111030846.DAA15245@smc.vnet.net>

soln = DSolve[{y''[x] == k y[x], y[0] == y0, y[10] == y10}, y[x], x][[1, 1]]

y[x] -> (E^(20*Sqrt[k])*y0 - E^(2*Sqrt[k]*x)*y0 - E^(10*Sqrt[k])*y10 +
        E^(10*Sqrt[k] + 2*Sqrt[k]*x)*
     y10)/(E^(Sqrt[k]*x)*(-1 + E^(20*Sqrt[k])))

soln /. y0 -> 0 // Simplify

y[x] -> ((-1 + E^(2*Sqrt[k]*x))*
    y10)/(E^(Sqrt[k]*(-10 + x))*(-1 + E^(20*Sqrt[k])))

soln /. y10 -> 0 // Simplify

y[x] -> ((E^(20*Sqrt[k]) - E^(2*Sqrt[k]*x))*
    y0)/(E^(Sqrt[k]*x)*(-1 + E^(20*Sqrt[k])))

soln /. {y0 -> 0, y10 -> 0}

y[x] -> 0

What solution are you expecting?


Bob Hanlon


On Thu, Nov 3, 2011 at 4:46 AM, 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}}
>

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