Degree of Differential Equation
The highest derivative of an equation, taking consideration of any coefficients or constants as well, is defined as the degree of the differential equation. It is the derivative in the equation with the highest power, in other words. When working with differential equations of the polynomial kind, determining a differential equation’s degree is important.
- For example, the equation (d2y/dx2)4+dy/dx=3
is a second-order differential equation with degree four because the highest order derivative is d2y/dx2 and its power is 4.
Speacial Case: Degree not Defined
Most of the time we can arrange the given differential equation in the form of polynomial where exponent is the order of differentiation, but for some differential equation this can be done. Those differential equations degree is not defined.
In other words, degree of a differential equation can only be defined if and only if the polynomial function of derivatives can be generated from the differential equation.
For example, sin(d2y/dx2) + dy/dx=0
is not a polynomial equation in derivatives because of the sine function. Therefore, its degree is not defined.
Some other examples of differential equation, where degree is not defined are:
- (d2y/dx2)2 3(dy/dx)3 = x log(d2y/dx2)
- x = sin(dy/dx – y cos x)
- x – ysin x = log(dy/dx)
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