Re: How to solve this equation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg72188] Re: How to solve this equation?*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 14 Dec 2006 05:49:02 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <eloqvd$o2j$1@smc.vnet.net>

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/