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