Re: Solving for a function in an Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg40796] Re: Solving for a function in an Integral
- From: Raibatak Das <rd54 at cornell.edu>
- Date: Thu, 17 Apr 2003 23:17:16 -0400 (EDT)
- References: <b7lmne$r41$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
sc - is the right hand side a definite integral? for an indefinite integral - the way you have posed it - the right hand side has some explicit dependence on t (except for the special case m[t]=constant). in that case, unless x depends on t the left hand side has no explicit t dependence and i'm not sure if there is going to be a legitimate solution. on the other hand, if x does depend on t and one knows the dependence then one could rewrite the entire equation in terms of x and solve it. i'm not sure if this is helpful at all, but if you could give a more specific case then it might be possible to try and figure out mathematica code to solve the problem. - rd. 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 > > ------------------------------------------------------------------------ * /Raibatak Das / * Department of Chemistry and Chemical Biology, Cornell University. Ithaca, NY 14853. Ph : 1-607-255-6141 email : rd54 at cornell.edu <mailto:rd54 at cornell.edu>