Consider the Clairaut equation for which g(y ') 1 4 (y ') 2 in Eq (37) Show that the line is tangent to the parabola Explain why this implies that y x 2 is a singular solution of the given Clairaut equation This singular solution and the one parameter family of straight line solutions are illustrat...

First the line y Cx has slope C and passes through t ...

Consider the Clairaut equation for which g(y') = -1/4 (y') 2 in Eq. (37). Show that the

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Consider the Clairaut equation

for which g(y') = -1/4 (y')² in Eq. (37). Show that the line

is tangent to the parabola

Explain why this implies that y = x² is a singular solution of the given Clairaut equation. This singular solution and the one-parameter family of straight line solutions are illustrated in Fig. 1.6.10.

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Differential Equations And Linear Algebra

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Authors: C. Edwards, David Penney, David Calvis

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Consider the Clairaut equation for which g(y') = -1/4 (y') 2 in Eq. (37). Show that the

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2 y=xy-(y)²

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