In this video there is detail concept of clairauts equation. Pdf clairaut antiinvariant submersions from normal. Clairaut who was the first to point out the difference between the general and the singular solutions of an equation of this form. Clairauts theorem on higher order partial derivatives. It is named after the french mathematician alexis clairaut, who introduced it in 1734. There is a special solution given parametrically by, with. Clairaut s theorem on higher order partial derivatives fold unfold. We investigate new clairaut conditions for antiinvariant submersions from normal almost contact metric manifolds onto riemannian manifolds. This handbook is intended to assist graduate students with qualifying examination preparation. Clairaut s theorem on higher order partial derivatives.
On implicit secondorder ordinary differential equations. It is a particular case of the lagrange differential equation. The equation is named for the 18thcentury french mathematician and physicist alexisclaude clairaut, who devised it. This is a clairauts equation with dependent variable and independent variable, so the solutions are. Overview in many respects, at least from an engineer s point of view. Pdf we investigate the new clairaut conditions for antiinvariant submersions whose total manifolds are cosymplectic. In this paper, we give a characterization of implicit secondorder ordinary differential equations with smooth complete integrals which we call clairauttype equations. The clairaut equation is a particular case of the lagrange equation when \\varphi \left y \right y. A clairaut equation is a firstorder equation of the form a remarkable feature of this nonlinear equation is that its general solution has a very simple form. The solution family for the general solution is, with. Solve the following differential equations by converting.