Variables Separable

Problem 05
$2y \, dx = 3x \, dy$,   when   $x = -2$,   $y = 1$.
 

Solution 05
From Solution 04,
$\dfrac{x^2}{y^3} = c$
 
 

Problem 03
$xy \, y' = 1 + y^2$,   when   $x = 2$,   $y = 3$.
 

Solution 03
$xy \, y' = 1 + y^2$

$xy \dfrac{dy}{dx} = 1 + y^2$
 

Problem 02
$2xy \, y' = 1 + y^2$,   when   $x = 2$,   $y = 3$.
 

Solution 2
$2xy \, y' = 1 + y^2$

$2xy \dfrac{dy}{dx} = 1 + y^2$

Problem 04
$2y \, dx = 3x \, dy$,   when   $x = 2$,   $y = 1$.
 

Solution 04
$2y \, dx = 3x \, dy$

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

Problem 01
$\dfrac{dr}{dt} = -4rt$,   when   $t = 0$,   $r = r_o$
 

Solution 01
$\dfrac{dr}{dt} = -4rt$

$\dfrac{dr}{r} = -4t\,dt$