Solved Problems on Order and Degree of Differential Equation
Problem 1: What is the order (if defined) and degree of the differential equation: d4y/dx4 + (d2y/dx2)2 – 3(dy/dx) + y = 9?
Solution:
Since d4y/dx4 is the highest order derivative, the order of this equation is 4, and degree is 1 as the highest order derivative has exponant 1.
Problem 2: Determine the order (if defined) and degree of the differential equation: [d2y/dx2 + (dy/dx)2]4 = k2(d3y/dx3)2.
Solution:
Since d3y/dx3 is the highest order derivative, the order of this equation is 3, and degree is 2 as the highest order derivative has 2 as it’s exponant.
Problem 3: Find the order (if defined) of the differential equation: √(d2y/dx2) + dy/dx = x.
Solution:
√(d2y/dx2) + dy/dx = x
⇒ √(d2y/dx2) = -dy/dx + x
⇒ d2y/dx2 = (-dy/dx + x)2
Since d2y/dx2 is the highest order derivative and it’s exponent is 1.
Thus, the order and degree of this equation is 2 and 1 respectively.
Problem 4: What is the order (if defined) and degree of the differential equation: dy/dx + (x2 + 5)y = x5?
Solution:
Because dy/dx is the highest order derivative and it’s exponent is 1, thus this equation has an order of 1 and degree 1 as well.
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