Problem 14 - 15 | Separation of Variables

$2y \, dx = 3x \, dy$

$2\dfrac{dx}{x} = 3\dfrac{dy}{y}$

$2\ln x = 3\ln y + \ln c$

$\ln x^2 = \ln y^3 + \ln c$

$\ln x^2 = \ln cy^3$

$x^2 = cy^3$           answer

$my \, dx = nx \, dy$

$m\dfrac{dx}{x} = n\dfrac{dy}{y}$

$m\ln x = n\ln y + \ln c$

$\ln x^m = \ln y^n + \ln c$

$\ln x^m = \ln cy^n$

$x^m = cy^n$           answer