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A second order differential equation is an equation that involves a second derivative of a function. It is often used to model physical phenomena such as motion, heat transfer, and electrical circuits.
The general form of a second order differential equation is y'' + p(x)y' + q(x)y = g(x), where y is the dependent variable, x is the independent variable, p(x) and q(x) are functions of x, and g(x) is a function of x.
There are several methods for solving a second order differential equation, such as separation of variables, variation of parameters, and using an integrating factor. The method used depends on the specific equation and initial conditions given.
Second order differential equations are used in many fields of science and engineering to model and predict behavior of physical systems. Some common applications include modeling population growth, predicting the motion of objects, and analyzing electrical circuits.
The initial conditions in a second order differential equation are the values of the dependent variable and its first derivative at a specific point in the independent variable. These values are often given as part of the problem and are used to find a specific solution to the equation.