Mister Exam

u(xx)-4u(xy)+5u(yy)-3u(x)+u(y)+u=0 canonical form

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u + u*y + u*x  - 3*u*x + 5*u*y  - 4*u*x*y = 0
$$u x^{2} - 4 u x y - 3 u x + 5 u y^{2} + u y + u = 0$$
u*x^2 - 4*u*x*y - 3*u*x + 5*u*y^2 + u*y + u = 0