MAT244--2018F > Thanksgiving Bonus

Thanksgiving bonus 6


Victor Ivrii:
Clairaut Equation
is of the form:
 To solve it we plug $p=y'$ and differentiate equation:
pdx= pdx + \bigl(x\varphi'(p) +\psi'(p)\bigr)dp \iff dp=0.
Then $p=c$ and
y=cx +\psi(c)
gives us a general solution.

(\ref{eq1}) can have a singular solution in the parametric form
&y=xp +\psi(p)
in the parametric form.

Find general and singular solutions to
$$y = xy’ +  ( y')^2.$$

Jiexuan Wei:
Here is my solution. :)

here is my solution

Victor Ivrii:
Cathy, the last thing you foub=nd was a singular solution, not a general one!


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