       Re: solve ODE help?

• To: mathgroup at smc.vnet.net
• Subject: [mg72141] Re: solve ODE help?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 13 Dec 2006 06:40:22 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <eljb9d\$7h0\$1@smc.vnet.net>

```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[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[y][x]+y Tan[x]==Sin[2x],y==2},y,x]
>
> but no help ? why?
> thanks
>

For differential equations, the functions that must be used are DSolve
 or NDSolve . (Especially, read the sections called "Further
Examples"). A general presentation can be found in The Mathematica Book.
(For instance see .) Detail explanations of all the intricacies can
be found in .

In:=
DSolve[{Derivative[y][x] + y[x]*Tan[x] == Sin[2*x]}, y, x]

Out=
{{y -> Function[{x}, C*Cos[x] - 2*Cos[x]^2]}}

In:=
DSolve[{Derivative[y][x] + y[x]*Tan[x] == Sin[2*x], y == 2}, y,
x]

Out=
{{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.