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

$(y \cos x~dx + \sin x~dy) - (2xy~dy + y^2~dx) = 0$

Problem 01 $x^3 - 3x^2y = c$

Solution 01

MATHalino