Examples of Order and Degree of Differential Equation
Let’s look at a few examples to better understand the order and degree of differential equations:
Example 1: dy/dx + 2x = 0
Answer:
Order: 1 (the highest derivative is the first derivative dy/dx)
Degree: 1 (the highest power of the derivative is 1)
Example 2: d2y/dx2 – 3(dy/dx)2+ 2x = 0
Answer:
Order: 2 (the highest derivative is the second derivative d2y/dx2)
Degree: 2 (the highest power of the derivative is 2)
Example 3: x2(d3y/dx3) + y3(dy/dx) = 0
Answer:
Order: 2 (the highest derivative is the second derivative d2y/dx2)
Degree: 2 (the highest power of the derivative is 2)
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