Table of Contents
What is the concept of differential equation?
In Mathematics, a differential equation is an equation with one or more derivatives of a function. The derivative of the function is given by dy/dx. In other words, it is defined as the equation that contains derivatives of one or more dependent variables with respect to one or more independent variables.
What are the concept and formation of differential equation?
A differential equation can be defined as an equation that consists of a function {say, F(x)} along with one or more derivatives { say, dy/dx}. The functions of a differential equation usually represent the physical quantities whereas the rate of change of the physical quantities is expressed by its derivatives.
What is the general solution of differential equation?
A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)
What is general solution of differential equation?
How important is differential equation in your chosen field and daily lives?
Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. They can describe exponential growth and decay, the population growth of species or the change in investment return over time.
What is the difference between general solution and particular solution?
Particular solution is just a solution that satisfies the full ODE; general solution on the other hand is complete solution of a given ODE, which is the sum of complimentary solution and particular solution.
What is a general solution of differential equation?
The general solution of the differential equation is the correlation between the variables x and y which is received after removing the derivatives (i.e. integration) where the relation includes arbitrary constants to represent the order of an equation.