Problem 51322. Solve an ODE: diffusion problem 1
In the solution of a problem involving diffusion, the following ordinary differential equation arises
where a is a positive constant and primes denote differentiation with respect to the independent variable η. The problem has the conditions and .
Write a function to solve this problem—that is, return values of f at specified values of η.
The physical problem involves diffusion of a quantity from one point where the concentration is maintained at a constant value into a medium in which the concentration is zero far away. The ODE results from transforming the diffusion equation—a partial differential equation in time and a spatial coordinate—with a similarity solution.
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