A second order differential equation is a mathematical equation that involves the second derivative of an unknown function. It represents the relationship between a function and its second derivative.
The main difference between a first and second order differential equation is the highest order derivative present in the equation. A first order differential equation has the first derivative of the unknown function, while a second order differential equation has the second derivative.
The general form of a second order differential equation is y'' = f(x,y,y'), where y is the unknown function, x is the independent variable, and y' and y'' represent the first and second derivatives of y, respectively.
Second order differential equations are used to model various physical systems, such as the motion of a pendulum, the growth of a population, and the oscillations of a spring. They are also used in engineering to design and analyze systems, such as electrical circuits and control systems.
Some common methods for solving second order differential equations include separation of variables, variation of parameters, and the use of Laplace transforms. Numerical methods, such as Euler's method and Runge-Kutta methods, can also be used to approximate solutions to these equations.