### Eliminate

Here are two slightly unusual applications of Eliminate.

#### Integro-Differential Equation

Consider the integro-differential equation

Mathematica has no built-in function for solving such equations. Jürgen Tischer (jtischer@col2.telecom.com.co) 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 (kuska@linmpi.mpg.de) 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

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