Answer to Question #105499 in Differential Equations for khushi

Question

State whether the following statements are true or false. Justify yourself with the help of
a short proof or a counter example(1)Equation x^2 ( y − px) = yp^2 is reducible to clairaut’s form

Answer 1

This statement is false. The Clairaut equation is $y=xp+f(p)$ where $p=y'$.

$x^2(y-px)=yp^2$ is reducible to form $y=xp+\frac{y}{x^2}f(p)$