Re: solve ODE help?

• To: mathgroup at smc.vnet.net
• Subject: [mg72238] Re: solve ODE help?
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Fri, 15 Dec 2006 07:06:52 -0500 (EST)
• References: <eljb9d\$7h0\$1@smc.vnet.net><eloqtg\$o1v\$1@smc.vnet.net>

```Among the list of references that Jean-Marc offered you see also the
following technical notes from
wolfram's site

http://library.wolfram.com/infocenter/TechNotes/18/
http://library.wolfram.com/infocenter/TechNotes/21/

Regards
Dimitris

Ï/Ç Jean-Marc Gulliet Ýãñáøå:
> learner wrote:
> >  Hi, everyone,
> >  i am new to solve ode in mathematica. i am trying to solve two
> > odes(not for hw :)).
> > y'+ytan(x)=sin(2x)
> >
> > I use: NSolve[{Direvative[1][y][x]+y Tan[x]==Sin[2x]},y,x]
> >
> > and get reply saying that:
> > InverseFunction::ifun: Inverse functions are being used. Values may be
> > lost for multivalued inverses
> >
> > {{y[x]->cot[x](sin[2x]-y'[x]}} ,
> > the mathematica did not solve the equation??
> >
> > Furthermore, I add condition that y==2 when x==0 by saying:
> >
> > NSolve[{Direvative[1][y][x]+y Tan[x]==Sin[2x],y[0]==2},y,x]
> >
> > but no help ? why?
> > thanks
> >
>
> For differential equations, the functions that must be used are DSolve
> [1] or NDSolve [2]. (Especially, read the sections called "Further
> Examples"). A general presentation can be found in The Mathematica Book.
> (For instance see [3].) Detail explanations of all the intricacies can
> be found in [4].
>
> In[1]:=
> DSolve[{Derivative[1][y][x] + y[x]*Tan[x] == Sin[2*x]}, y, x]
>
> Out[1]=
> {{y -> Function[{x}, C[1]*Cos[x] - 2*Cos[x]^2]}}
>
> In[2]:=
> DSolve[{Derivative[1][y][x] + y[x]*Tan[x] == Sin[2*x], y[0] == 2}, y,
>    x]
>
> Out[2]=
> {{y -> Function[{x}, -2*(-2*Cos[x] + Cos[x]^2)]}}
>
> Regards,
> Jean-Marc
>
> 1. http://documents.wolfram.com/mathematica/functions/DSolve
>
> 2. http://documents.wolfram.com/mathematica/functions/NDSolve
>
> 3. http://documents.wolfram.com/mathematica/book/section-1.5.9
>
> 4.