Bessel coefficients 13 functions 4 integral function

Sometimes an equation out of this classification can be altered to fit by change of variable. The equations with separable variables are solved with a table of integrals or by numerical means. Higher order linear equations with constant coefficients are solvable with the aid of Laplace Transforms. Some complex equations may be solvable by series expansions or in terms of higher functions, for instance the Bessel equation encountered in problem P7.02.07, or the equations of problem P2.02.17. In most cases a numerical solution Is possible. 

Activity coefficients on the molal scale were calculated from Equation 39 by means of a straightforward program containing library sub-routines for evaluation of integrals and modified Bessel functions. 

Problem 3-1. Flow in a Cylindrical Tube. Re-solve the start-up of a pressure-driven flow through a tube of radius R, only this time take the pressure gradient to be G = A t2 for all t > 0, where A is a constant. You may obtain the asymptotic solution at large time by recognizing that Moo = f (r)t2 + fi(r)t + Mr)- Obtain an integral expression for the coefficients of the decaying solution, but don t evaluate the integral unless you want practice with Bessel functions. 

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