Question

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

Answer 1

$U=-\frac{2y^{2} }{x^{2} -4x-3y} \\\\x =\frac{2U+\sqrt{U(4U-2y^{2}+3Uy) } }{U} \\x=\frac{2U-\sqrt{U(4U-2y^{2}+3Uy) } }{U}\\\\y =\frac{3U+\sqrt{U(9U-8x^{2} +32x} }{4\\}\\y=\frac{3U-\sqrt{U(9U-8x^{2} +32x} }{4\\}$