Do you find some equations very complex to solve? Well, a differential equation can ease your problems. Here you will be able to find the methods to find the orders and degrees and will be able to solve different types of differential equations. Let’s study more in the topics below.
- Order and Degree of Differential Equations
- Homogeneous Differential Equations
- Linear Differential Equations
- General and Particular Solutions of a Differential Equation
- Formation of differential Equation whose General Solution is Given
- Differential Equations with Variables Separable
Question: State the use of differential equation?
Answer: These equations have an amazing capability to predict the world around us. Furthermore, we use them in a wide variety of disciplines, from biology, physics, chemistry, economics, and engineering. Moreover, they can describe exponential growth and decay, the population growth of species.
Question: Mention the types of differential equations?
Answer: The various types of differential equations are:
- Ordinary differential equations
- Partial differential equations
- Linear differential equations
- Non-linear differential equations
- Homogenous differential equations
- Non-homogenous differential equations
Question: State the first order of differential equation?
Answer: To begin with, the first-order differential equation is an equation \(\frac{dy}{dx} = f(x,y)\), in which f(x, y) is a function of two variables defined on a region in the xy-plane. However, this is a first-order equation because it involves only the first derivative dy/dx (and not higher-order derivatives).
Question: Why do we need partial differential equations?
Answer: We need to use partial differential equations to mathematically formulate, and therefore assist the solution of, physical and other problems that involve functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrodynamics, electrostatics, etc. Moreover, these mathematical equation requires two or more independent variables, an unknown function, and partial derivatives of the known function.