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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[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.
http://documents.wolfram.com/mathematica/Built-inFunctions/AdvancedDocumentation/DifferentialEquations/
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