Welcome to our community

Be a part of something great, join today!

Clairaut's equation

suvadip

Member
Feb 21, 2013
69
Please help me to find the singular solution of the following Clairaut's equation

\(\displaystyle y=px+\sqrt{1+2p^4}\) where \(\displaystyle p=\frac{dy}{dx}\)
 
Last edited by a moderator:

suvadip

Member
Feb 21, 2013
69

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
I can express as x=f(p) and y=g(p). But I cant eliminate p to find a relation between x and y.
Is it necessary to express the singular solution in implicit form?. You can write it in parametric form: $$x=\dfrac{-4p^3}{\sqrt{1+2p^4}},\quad y=\dfrac{1-2p^4}{\sqrt{1+2p^4}}$$