Differential equations of the form

dy/dx = – P(x)/Q(y)

then it is possible to separate the variables

Q(y)dy = – P(x) dx → Q(y) dy + P(x) dx = 0

Ex

y´+ sinx y = 0

y´ = -sinx y

dy/y = -sinx dx

Integrating both sides

lny = cosx +C

y = De^cosx