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MathGroup Archive 2007

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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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