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Re: Solving differential equations with parameters
*To*: mathgroup at smc.vnet.net
*Subject*: [mg79807] Re: [mg79786] Solving differential equations with parameters
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Sun, 5 Aug 2007 04:51:44 -0400 (EDT)
*Reply-to*: hanlonr at cox.net
Off[Solve::ifun];
soln[x_, p_, y0_] =
Simplify[y[x] /.
DSolve[{y'[x] == -Sin[p*x + y[x]], y[0] == y0}, y[x], x][[1]]]
2*ArcTan[(Sqrt[p^2 - 1]*Tan[(1/2)*Sqrt[p^2 - 1]*x +
ArcTan[(p*Tan[y0/2] - 1)/Sqrt[p^2 - 1]]] + 1)/p] -
p*x
y'[x] == -Sin[p*x + y[x]] /. {y[x] -> soln[x, p, y0],
y'[x] -> D[soln[x, p, y0], x]} // FullSimplify
True
Plot3D[soln[x, p, 0], {x, 0, 1}, {p, 0, 2}]
Plot3D[soln[x, p, 2*ArcTan[1/p]], {x, 0, 1}, {p, 0, 2}]
Bob Hanlon
---- Ivan <darknails at gmail.com> wrote:
> Hi, I am trying to solve the differential equations like
>
> y'[x]= - Sin[ p*x + y[x] ]
>
> where p is a parameter. Now I want to solve the equation with respect
> to x for a range of values of p, instead for just a single p.
> What is the best way to do it?
>
>
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