Reduce-the-equations-to-Clairaut-s-form-and-find-the-general-solution-x-2-p-2-yp-2x-y-y-2-0-put-y-u-and-xy-v-

Question Number 85116 by niroj last updated on 19/Mar/20

Reduce the equations to {Clairaut}^{'} s form

and find the general solution :

x^{2} p^{2} + yp (2 x + y) + y^{2} = 0 (p u t y = u a n d x y = v)

Commented by MJS last updated on 19/Mar/20

{what}^{'} s the general solution of an equation

with 3 unknowns ?

p = - \frac{(2 x + y) y}{2 x^{2}} \pm \frac{\sqrt{(4 x + y) y^{3}}}{2 x^{2}}

x = y (- \frac{1}{p} \pm \frac{1}{\sqrt{- p}})

y = x (- \frac{p}{p + 1} \pm \frac{\sqrt{- p^{3}}}{p + 1})

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