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Re: NDSolve[]

• To: mathgroup at smc.vnet.net
• Subject: [mg123535] Re: NDSolve[]
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sat, 10 Dec 2011 07:30:10 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201112091058.FAA03928@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

The first method has invalid syntax for Derivative. Here are three correct  
solutions:

{x1, y1} = {x, y} /.
    First@NDSolve[{Derivative[1][x][t] == -y[t] - x[t]^2,
       Derivative[1][y][t] == 2*x[t] - y[t], x[0] == y[0] == 1}, {x,
       y}, {t, 10}];
{x2, y2} = {x, y} /.
    First@NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2*x[t] - y[t],
       x[0] == y[0] == 1}, {x, y}, {t, 10}];
{x3, y3} = {x, y} /.
    First@NDSolve[{D[x[t], t] == -y[t] - x[t]^2,
       D[y[t], t] == 2*x[t] - y[t], x[0] == y[0] == 1}, {x, y}, {t,
       10}];
Row@{Plot[{x1@t, y1@t}, {t, 0, 10}, ImageSize -> 250],
   Plot[{x2@t, y2@t}, {t, 0, 10}, ImageSize -> 250],
   Plot[{x3@t, y3@t}, {t, 0, 10}, ImageSize -> 250]}

Bobby


> Z
> Subject: NDSolve[]
> To: mathgroup at smc.vnet.net
>
> For the same equations, why does the first method as following give
> the error but the other one give the desired result?
>
> NDSolve[{Derivative[x[t], t] == -y[t] - x[t]^2,
>   Derivative[y[t], t] == 2*x[t] - y[t], x[0] == y[0] == 1}, {x,
>   y}, {t, 10}]
>
> NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2*x[t] - y[t],
>   x[0] == y[0] == 1}, {x, y}, {t, 10}]
>


-- 
DrMajorBob at yahoo.com

• References:
  • [no subject]
    • From: "Steven M. Christensen" <steve@smc.vnet.net>