Show system of PDEs has no solution

[perishingtardi]

Homework Statement

Show that there is no solution for the system
$$u_x - 2.999999x^2 y + y = 0,$$
$$u_y - x^3 + x = 0.$$

Homework Equations

The Attempt at a Solution

I took the first equation and integrated w.r.t x, then differentiated w.r.t y. But I'm not sure if it helps:
$$u_y - \frac{2.999999}{3}x^3 + x = f'(y)$$ where f(y) is an arbitrary function of y.

 

[pasmith]

Homework Statement

Show that there is no solution for the system
$$u_x - 2.999999x^2 y + y = 0,$$
$$u_y - x^3 + x = 0.$$

Homework Equations

The Attempt at a Solution

I took the first equation and integrated w.r.t x, then differentiated w.r.t y. But I'm not sure if it helps:
$$u_y - \frac{2.999999}{3}x^3 + x = f'(y)$$ where f(y) is an arbitrary function of y.

And can you choose $f(y)$ such that $u_y - x^3 + x = 0$, as required?