Show that the given solution is correct by directly substituting it into the quasilinear PDE:

solution: u-y = F(x + (y/u) - log(u))

PDE: y(du/dx) + u^2 (du/dy) = u^2

My workings are as follows:

du/dx = F'(arg)(1 - y/u^2(du/dx) - 1/u(du/dx)) and du/dy = 1 + F'(arg)(((u-y)*(du/dy)/u - 1/u du/dy)

Subbing this into the PDE and cancelling terms I end up with a non-identity. Are these derivitatives du/dx and du/dy correct?