Re: Partial Derivatives
- To: mathgroup at smc.vnet.net
- Subject: [mg7927] Re: [mg7774] Partial Derivatives
- From: jpk at max.mpae.gwdg.de
- Date: Wed, 23 Jul 1997 15:46:07 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Hi > I am trying to find partial derivatives of > an equation, eg y''[x] + y'[x] + x^2 ==0. > What I would like is to say something like pD[eqn,y[x]] and get back 0 > while pD[eqn,y''[x]] will give me 1. Certainly D does this. What do You want ? Coefficient[eqn[[1]],y''[x]] gives 1 and Coefficient[eqn[[1]],y[x]] gives 0 It is a miss use of derivatives to find the coefficients. > However, > I also want pD[eqn,x] to give me 2x and not y'''[x] + y''[x] + 2 x. > Can anyone please suggest a way to get around this? Yes, invent a new kind of differential calculus. Newton and Leibniz have it done -- just try it again. D[ y''[x] + y'[x] + x^2,x] == y'''[x] + y''[x] + 2 x is correct in the common sense of differntial calculus. How ever it is up to You to invent a new one. > > Note that entering the equation as y'' + y' + x^2 does not work. Here > D[eqn,y] gives me the strange result y''' + y'' which I really cannot > understand. If the input is strange the result of any operation on it will probably not become better. What is y' ? d y --- (??) d ? You can not made a derivative on a symbol with respect to nothing. You can look for the total derivative with Dt[y] of a symbol. Hope that helps Jens