Question

Solve: (x² – yx²) dy + (y² + xy²) dx = 0 

Answer 1

Given differential equation is :

(x² - yx²)dy + (y² + xy²)dx = 0

⇒ x²(1-y)dy + y² (1+x)dx = 0 

⇒ `int(1-"y")/"y"^2 "dy" + int(1+"x")/"x"^2 "dx" = 0`

⇒ `int(1/"y"^2 - 1/"y")"dy" + int(1/"x"^2 + 1/"x")"dx" = 0`

⇒ `int"y"^-2"dy" - "log" "y" + int"x"^-2"dx" + "log x" = 0`

⇒ `"y"^-1/-1 - "log y" + "x"^-1/-1 + "log x" = C`

⇒ `-1/"y" - "log y" - 1/"x" + "log x" = C`

⇒ `- 1/"x" - 1/"y" + "log"("x"/"y") = C`