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/