(x-1)(y+1)y'-(2x-1)(2y+1)=0

Question

(x-1)(y+1)y'-(2x-1)(2y+1)=0

Comments

Это что? Диф уравнение?

Answer 1

Ху+х-у-1-4ху-2х+2у+1=0
-3ху-х+у=0

Answer 2

(x-1)(y+1)y' - (2x-1)(2y+1) = 0
(x-1)(y+1)dy/dx = (2x-1)(2y+1)
 (y+1)/(2y+1)dy = (2x-1)/(x-1)dx
[(y + 1/2)/(2y+1) + (1/2)/(2y+1)]dy = [(2x-2)/(x-1) + 1/(x-1)]dx
[2 + 1/(y+1/2)]dy = 4*[2 + 1/(x-1)]dx
2y + ln|y+1/2| = 8x + 4ln|x-1| + ln|C/2|
(2y+1)*e^(2y) = C*(x-1)^4 * e^(8x)