Here are two slightly unusual applications of Eliminate.
Consider the integro-differential equation
Mathematica has no built-in function for solving such equations. Jürgen Tischer (email@example.com) suggested the following elegant approach. Differentiating with respect to
and eliminating the integral yields a trivial differential equation.
The solution to this equation for the pair of initial conditions, and , is immediate.
It is easy to verify that this solution satisfies the integro-differential equation.
System of Differential Equations
Consider a system of differential equations.
It should be apparent that and can be eliminated from this linear system of equations. Jens-Peer Kuska (firstname.lastname@example.org) suggested an elegant method for doing this using Eliminate. After differentiating the system of equations,
we can then eliminate , , and .
Converted by Mathematica September 30, 1999 [Prev Page][Next Page]