Re: Differential equations and notation

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: Differential equations and notation*From*: winkel at nextwork.rose-hulman.edu*Date*: Fri, 16 Oct 92 17:11:58 EST

Hello I enjoy reading a number of user group activities. One of them is the Maple group. I recently found this message of interest. >I am trying to know if Maple can solve the following equation: > g:=(a*t^2+b)*diff(diff(f(t),t),t)+c*t*diff(f(t),t)+d*f(t)=e; > >with values > a:=335/10000; > c:=154/1000; > b:=129/1000; > d:=46872/1000; > e:=544/10000; There was some reply indicating Maple would not solve this equation. I tried the equation on Mathematica and it would not DSolve it either. It quickly (1.05 seconds) NDSolve'd the differential equation with initial conditions f(0 = 1 and f'(0) = 1) in the t interval [0, 5] and I used Mathematica's resulting InterpolatingFunction solution to plot out a nice wavy graph. I also noted the author of a response to the original problem indicated there is a solution in terms of hypergeometric functions which readily exist in Mathematica as well. My point is not the differential equation per se, but notation. I understand the choice of computer algebra systems (e.g. Maple) or systems for doing mathematics by computer (Mathematica) can be akin to religion. Moreover, I understand Mathematica has its share of cumbersome notation. But I could not help but look at the statement of a differential equation above in Maple syntax: (a*t^2+b)*diff(diff(f(t),t),t)+c*t*diff(f(t),t)+d*f(t)=e and compare it to the corresponding syntax both visually and mathematically in Mathematica (a t^2 + b) f''[t] + c t f'[t] + d f[t] == e. Brian J. Winkel, Editor PRIMUS, Cryptologia, Collegiate Microcomputer Department of Mathematics Rose-Hulman Institute of Technology Terre Haute IN 47803 USA PHONE: 812-877-8412: FAX 812-877-3198 email: winkel at nextwork.rose-hulman.edu