# Method of Variable Separation

If the coefficient of dx is only a function of x and that of dy is only a function of y in the given differential equation, then the equation can be solved using variable separation method

Thus the general form of such an equation is

f(x) dx + g(y) dy = 0  ...(3)

Integrating, we get dy = c; where c is the arbitrary constant. This is a general solution of (3).

# Differential equations reducible to the separable variable type

Sometimes differential equation of the first order cannot be solved directly by variable separation. By some substitution we can reduce it to a differential equation with separable variable. A differential equation of the form = f(ax + by + c) is solved by putting ax + by + c = t.