Question

Uxx - 2xy - Uyy + 4Ux + 3Uy=0

Answer 1

$U=\frac{2xy}{y^{2}-4x-3y }\\\\ x=\frac{Uy^{2}}{2(-y+2U)} -\frac{3Uy}{2(-y+2U)} \\\\y=-\frac{2x-3U+\sqrt{4x^{2} -12xU+9U^{2}+16U^{2}x } }{2U} \\y=-\frac{2x-3U-\sqrt{4x^{2} -12xU+9U^{2}+16U^{2}x } }{2U}$