Show system of PDEs has no solution

  • #1
perishingtardi
21
1

Homework Statement


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


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:
[tex]u_y - \frac{2.999999}{3}x^3 + x = f'(y)[/tex] where f(y) is an arbitrary function of y.
 

Answers and Replies

  • #2
pasmith
Homework Helper
2,271
877

Homework Statement


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


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:
[tex]u_y - \frac{2.999999}{3}x^3 + x = f'(y)[/tex] where f(y) is an arbitrary function of y.

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

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