First-order second-degree equations related with Painlevé equations

The first-order second-degree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlev´e equations, and one-parameter families of solutions which solve the first-order second-degree equations are investigated.The first-order second-degree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlev´e equations, and one-parameter families of solutions which solve the first-order second-degree equations are investigated

Painlevé test and higher order differential equations

Abstract Starting from the second Painlevé equation, we obtain Painlevé type equations of higher order by using the singular point analysis