first order differential equation

Problem 04
$cy^2 = x^2 + y$
 

Problem 04
$cy^2 = x^2 + y$       → equation (1)

$2cy~dy = 2x~dx + dy$

$c = \dfrac{2x~dx + dy}{2y~dy}$
 

Problem 03
$x^2y = 1 + cx$
 

Solution 03
$x^2y = 1 + cx$       → equation (1)

$x^2~dy + 2xy~dx = c~dx$
 

Problem 02
$y \sin x - xy^2 = c$
 

Solution 02