# 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 methodThus 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*.