Separable Differential Equation

What is Variable Separable Differential Equation in Calculus?

Generally, the differential equation of the form dy/dx = f(x)/g(y) is called a variable separable differential equation. In these equations, we can easily separate both variables and the differential variable and can arrange them on either side of the equal sign (=).

How to Identify Separable Differential Equation?

We can easily identify the separable differential equation by separating the independent variable and dependent variable on either side of the equal sign. If we are able to separate the variables then the equation is a separable differential equation.

How to solve Separable Differential Equation?

Separable differential equations are easily solved by arranging all the dependent variables on one side of the equal sign and the independent variable on the opposite side of the equal sign and then integrating both sides separately to get the final answer.

What is the Difference between Linear and Separable Differential Equation?

• Differential equation where the power of the derivative dy/dx is one and they are written in the form, dy/dx + Py = Q is called Linear Differential Equation.
• Equation in which we can easily separate the dependent variable and the independent variable along with their differential variable is called the separable differential equation

What are Non-Separable Differential Equation?

All the differential equations where we can not separate the independent variable (x) and the dependent variable (y) are called the non-separable differential equation.

How to Solve Non-Separable Differential Equation?

We can solve the non-separable differential equations by various methods which are,

• Using the Homogenous Differential Equation method.
• Using the Exact Differential Equation method.
• Using the Linear Differential Equation method.

Separable differential equations are a special type of ordinary differential equation (ODE) that can be solved by separating the variables and integrating each side separately. Any differential equation that can be written in form of y’ = f(x).g(y), is called a separable differential equation.

Basic form of the Separable differential equations is dy/dx = f(x) g(y), where x is the independent variable and y is the dependent variable.