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Re: solve ODE help?


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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