The Maple solver …

$.getScript('/s/js/3/uv.js'); We have the following: We first note that the expression whose cosine is being taken is the derivative of , hence the natural choice of substitution is to try for . } catch (ignore) { }

defines only one solution y(x), the so-called singular solution, whose graph is the envelope of the graphs of the general solutions. The singular solution is usually represented using parametric notation, as (x(p), y(p)), where p = dy/dx. $(window).on('load', function() { [1], 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. Our next step is to try and write in terms of and . ga('send', 'event', 'fmlaInfo', 'addFormula', $.trim($('.finfoName').text()));

Hence, either d 2 y d x 2 = 0 or x + f ′ (d y d x) = 0.

The following curves represent the solutions to two Clairaut's equations: In each case, the general solutions are depicted in black while the singular solution is in violet. Autoencoders are unsupervised deep learning neural network algorithms that reduce the number of dimensions in the data to encode it. try { }); Clairaut’s theorem is a general mathematical law applying to spheroids of revolution.

Rather, we need to plug these solutions into the original equation to constrain them. The value of the acceleration of gravity at the equator, The ratio of the centrifugal force to gravity at the equator, The flattening of a meridian section of the earth.

Clairaut’s formula is giving the acceleration due to gravity g on the surface of a spheroid at latitude φ.

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