Nonautonomous Lienard systems equivalent to first-order differential equations

Abstract

AbstractGenerally, second-order differential equations are mapped onto first-order equations to determine their solutions. In the present paper, first-order differential equations with well-known analytic properties are transformed into new or known nonautonomous Lienard differential equations to obtain their exact solutions using the theory of second-order differential equations based on the existence of a first integral recently introduced in the literature by the present authors. First-order differential equations that appear in the Kamke book are used as illustrative examples. As a result, these examples show that parametrically excited Lienard equations may not exhibit parametric resonance.