Airy differential equation

The method described for example 3.4 can be used to solve boundary value problems. Consider the boundary value problem given by the Airy differential equation ... 

The solution of plane (two-dimensional) elasticity problem now resides in the determination of an Airy stress function (h(x, y) that satisfies the governing fourth-order partial differential equation and the appropriate boundary conditions. Note that ... 

G. B. Airy s little book,. An Elementary Treatise on Partial Differential Equations, London, 1873, will repay carefnl study in connection with the geometrical interpretation of the solutions of partial differential equations. 

When the coefficient of the differential equation is an nth-order polynomial, the n + 2 Stokes lines run radially in the asymptotic region. There are thus n + 2 unknown Stokes constants, but only three independent conditions are obtained from the singlevaluedness as demonstrated for the Airy function. 

---