The formula can be used to relate the gravity at any point on the Earth’s surface to the position of that point, allowing the ellipticity of the Earth to be calculated from measurements of gravity at different latitudes. // event tracking (The flattening of a meridian section of the earth is defining as the ratio of the difference between the semimajor axis and the semiminor axis to the semimajor axis f=(a-b)/a ) \$(window).on('load', function() { By extension, a first-order partial differential equation of the form, "Solution de plusieurs problèmes où il s'agit de trouver des Courbes dont la propriété consiste dans une certaine relation entre leurs branches, exprimée par une Équation donnée. Clairaut's formula is giving the acceleration due to gravity g on the surface of a spheroid at latitude φ. The Clairaut equation is a particular case of the Lagrange equation when φ(y′) = y′. the so-called general solution of Clairaut's equation. Recall that and , so , so , so: This is a Clairaut's equation with dependent variable and independent variable , so the solutions are: https://calculus.subwiki.org/w/index.php?title=Clairaut%27s_equation&oldid=2099, Clairaut's theorem on equality of mixed partials, The solution family for the general solution is, There is a special solution given parametrically by. To solve Clairaut's equation, one differentiates with respect to x, yielding The plot shows that here the singular solution (plotted in red) is an envelope of the one-parameter family of solutions making up the general solution. That gives you the equation of y"(x + f'(y'))=0. The clue is in the name really, autoencoders encode data. The singular solution is usually represented using parametric notation, as (x(p), y(p)), where p = dy/dx. }); , To solve Clairaut's equation, one differentiates with respect to x, yielding, In the former case, C = dy/dx for some constant C. Substituting this into the Clairaut's equation, one obtains the family of straight line functions given by. Rather, we need to plug these solutions into the original equation to constrain them. ga('send', 'event', 'fmlaInfo', 'addFormula', \$.trim(\$('.finfoName').text())); Clairaut's equation is a first-order differential equation of the form: Here, is a suitable function. window.jQuery || document.write('