In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow.
It is named after mathematicians Leonhard Euler and Francesco Giacomo Tricomi.
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.
A general expression for particular solutions to the Euler–Tricomi equations is: where
These can be linearly combined to form further solutions such as: for k = 0: for k = 1: etc.