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Re: How to solve this equation?


learner wrote:
> hi,
> I am trying to solve  y'+y tanx=sin(2x)
> 
> i wrote NSolve[{Derivative[1][y][x]+y Tan[x]==Sin[2x]},y,x] but get
> something like
> 
> {{y->cot[x](sin[2x]-y`[x]}}
> 
> I want to set a restraint to say y=2 when x=0, how shoud i do it?
> 
> many 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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