Variables separable method of Differential equations

A method of solving a differential equation by separating the functions in one variable from the functions in another variable is called the method of solving the differential equation by the separation of variables.

Introduction

In calculus, the differential equations are formed by the functions in two variables along with differential elements. The best way to solve the differential equations is, bringing the functions in one variable along with respective differential on one side of the equation and keeping the functions in another variable with corresponding differential element on the other side of the equation.

It helps us to separate the functions in one variable from the functions in another variable. Hence, this method is called the variables separable or the separation of variables. The separation of variables method is mathematically expressed in the following two forms.

$(1).\,\,\,$ $\displaystyle \int{\phi{(y)}\,}dy \,=\, \int{f(x)\,}dx+c$

$(2).\,\,\,$ $\displaystyle \int{\dfrac{1}{h(y)}\,}dy$ $\,=\,$ $\displaystyle \int{g(x)\,}dx+c$

Problems

The list of separation of variables questions with solutions to learn how to solve the differential equations.