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.