Technique used to solve certain types of

differential equations. This technique involves collecting all of the variables in the equation with their corresponding d.

Rei:

x dy + y dx=0
x dy=-y dx <- organizing equation
dy/y = -dx/x <- dividing by x and y - separating equation
Sdy/y=-Sdx/x <- integrate both sides
ln|y| + c_{1} = -ln|x| + c_{2} <- fundamental theorem of Calculus
ln|y|+ln|x| = C <- collecting constants
e^(ln|y*x|)= e^C <- simplifying
y*x=C_{2} <- simplifying further - new constant
y=C_{2}/x