# Euler–Tricomi equation

In mathematics, the **Euler–Tricomi equation** is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi.

It is elliptic in the half plane *x* > 0, parabolic at *x* = 0 and hyperbolic in the half plane *x* < 0.
Its characteristics are

which have the integral

where *C* is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line *x* = 0, the curves lying on the right hand side of the *y*-axis.

## Contents

## Particular solutionsEdit

Particular solutions to the Euler–Tricomi equations include

where *A*, *B*, *C*, *D* are arbitrary constants.

A general expression for these solutions is:

where

The Euler–Tricomi equation is a limiting form of Chaplygin's equation.

## See alsoEdit

## BibliographyEdit

- A. D. Polyanin,
*Handbook of Linear Partial Differential Equations for Engineers and Scientists*, Chapman & Hall/CRC Press, 2002.

## External linksEdit

- Tricomi and Generalized Tricomi Equations at EqWorld: The World of Mathematical Equations.