Re: Solving for a function in an Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg40794] Re: Solving for a function in an Integral
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Thu, 17 Apr 2003 23:17:07 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <b7lmne$r41$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, where in d[x]== Sin[x]*Integrate[Cos[m[t]],t]+Cos[x]*Integrate[Sin[m[t]],t] is the problem ? This is a algebraic equation for d[x] -- that you integrate something for f[1][t]=Integrate[Cos[m[t]],t] f[2][t]=Integrate[Sin[m[t]],t] in d[x]== Sin[x]*f[1][t]+Cos[x]*f[2][t] does not turn your equation into an differential equation. You should tell us if d[x] and/or m[x] are known functions. If both are unknown you miss an equation to get a solution. Regards Jens You can try to build succsessive derivatives and solve the differential equation Steven Clarke wrote: > > Hi all > > I'm wondering if there is a way to solve for a function within an integral. > > Specificly, I have something like this: > > d[x] == Integrate[Sin[x + m[t]],t] > > so I have function d, dependent on x, which is equal to the integral of > sin[x + m[t]] with respect to t, when m[t] is a function of t. > > It looks sort of like a differential equation, but not really, and DSolve > didn't like it. I thought about taking the derivative of both sides with > respect to t, but then the d[x] just goes completely away, and that can't > work. > > Is this problem mathmatically possible, and if so, what kind of problem is > it (ie, ODE, Partial Differential Equations, something else) so I can go > look up a book on those types of problems, and finally, can Mathmatica solve > this type of problem? > > Thanks > > Steve