How To Find Order and Degree Of Differential Equation?
To find the order and degree of Differential Equation, we can use the following steps:
Step 1: Examine the Differential Equation.
Step 2: Write the Differential Equation in Standard Form.
Step 3: Determine the Order.
Step 4: Determine the Degree.
Let’s consider an example for better understanding.
Example: Find the order and degree of the following differential equation.
3(d2y/dx2)2 – 3 = 4xdy/dx
Answer:
Step 1: Examine the Differential Equation.
After examination of the given Differential Equation, we get to know there are two derivative terms in the equation i.e., d2y/dx2, and dy/dx.
Step 2: Write the Differential Equation in Standard Form.
To write the Differential Equation in Standard Form i.e., in the decreasing order of differentiation just like polynomial.
Thus, the given equation becomes,
3(d2y/dx2)2 – 4xdy/dx – 3 = 0
Step 3: Determine the Order.
The order of the differential equation is the highest order of derivative present. In this case, the highest order of derivative is the second derivative, so the order is 2.
Step 4: Determine the Degree.
The degree of the differential equation is determined by the highest power of the highest order derivative present. In this case, the second derivative i.e., d2y/dx2 is raised to the power of 2, so the degree is also 2.
Thus, for equation 3(d2y/dx2)2 – 3 = 4xdy/dx, order and degree both are 2.
Read More,
Order and Degree of Differential Equations
Order and Degree of differential equations indicate the degree of complexity and the number of independent variables in the differential equations. The highest derivative sets the order of the equation and offers important information about the function’s behaviour and evolution. It is an important tool for dealing with scientific and engineering problems, with applications in physics, engineering, biology, and economics.
Understanding the order and degree of differential equations allows us to foresee how the function will react to changes in independent variables, allowing us to better comprehend complex systems and real-world occurrences. This inquiry delves into the significance and applications of the “Order and Degree of Differential Equations,” helping us to better comprehend the intricacies of our surroundings.
Table of Content
- What are Differential Equations?
- Order of Differential Equation
- First Order Differential Equation
- Second Order of Differential Equation
- Degree of Differential Equation
- How To Find Order and Degree Of Differential Equation?
- Examples of Order and Degree of Differential Equation