My question is
If $u(x,y)$ and $v(x,y)$ are two integrating factors of a diff eqn $M(x,y)dx + N(x,y)dy$, $u/v$ is not a constant. then $u(x,y) = cv(x,y)$is a solution to the differential eqn for every constant $c$. I m totally stuck :(
Another doubt i have is how to derive the singular solution for the Clairaut's equation. i tried it we have $y= px + f(p)$ diff wrt $x$ and considering $dp/dx=0$ we get $p=c$, how to solve the other part?