Solving Differential Equations in Variable Separable Form

General differential equation of first order and first degree is of the form

M + Ndy/dx = 0

Where M and N are any functions of x and y.

If M = f(x) and N = g(y), the equation can be written as

f(x) + g(y)dy/dx = 0

=>
g(y)dy = -f(x)dx

Integrating both sides

∫g(y)dy = ∫-f(x)dx +c

When the M and N can be separated into f(x) and g(y), the equation is called as an equation with separable variable