Short Notes on Differential Equation: Order, Degree & Solutions

By Avinash Kumar|Updated : September 5th, 2017

An equation involving independent variable(x), dependent variable(y) and derivative of dependent variable with respect to independent variable is called a differential equation. For example


Now let's see some basic properties of differential equation. These are called Order and Degree of differential equation.

Order and Degree of a Differential Equation

The order of a differential equation is the derivative of the highest order in the differential equation.

And the degree of a differential equation is the degree of the highest order (Power of the highest order term) differential coefficient appearing in it, provided it can be expressed as a polynomial equation in derivatives.

Order and degree are Integers, not fraction. If we see power in fraction, then make them integer by squaring or cube or etc.

For Example: -

  • Here the order is 3 and degree is 4.

  • Here we can see that the order is 2 but degree is in fraction form so we can write this as

    So the degree is 3.

If we want to make a differential equation from a general solution then all we need to do is use simple differentiation and convert solution into a differential equation. 

Solution of differential equations

So there are 2 type of solution one is called general solution and other is called particular solution.  

If the solution of differential equation which contains arbitrary constants as many as the order of the differential equation and it is called general solution. And if we know that particular values of the arbitrary constants in the general solution then it is called particular solutions.

 As we know that in the general integral we add arbitrary constant. So in the general solution we add constant in every integral. So if a differential equation is “n” order then we must see “n” arbitrary constant in the solution.

Stay tuned for more.

Click on the links below to read more about Differential Equations:

How to Solve Differential Equations by Variable Separable Method

How to Solve Homogeneous Differential Equation

How to Solve Linear Differential Equations

Click on the links below to access the list:

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Avinash KumarAvinash KumarMember since Feb 2017
Don't quit, suffer now and live the rest of your life as a champion. -Muhammad Ali
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