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chwala
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Homework Statement
how do we establish failure of uniqueness on this first order differential equation
## y(x)= x y'+(y')^2##
Homework Equations
The Attempt at a Solution
[/B]
general solutions are ## y= cx^2+c^2## where c = constant and
## y= -0.25x^2##
## -0.25x^2+cx+4c^2=0##
##x= -2c ⇒ y=-c^2## for failure of uniqueness the two solutions intersect at the above points...any other alternative methods?
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