![]() Second Order Differential Equation Definition What is a Second Order Differential Equation? We will also learn different methods to solve second order differential equations with constant coefficients using the various methods with the help of solved examples and finding the auxiliary equation. In this article, we will understand such differential equations in detail and their different types. The differential equation y'' + p(x)y' + q(x)y = 0 is called a second order differential equation with constant coefficients if the functions p(x) and q(x) are constants and it is called a second-order differential equation with variable coefficients if p(x) and q(x) are not constants. We can solve this differential equation using the auxiliary equation and different methods such as the method of undetermined coefficients and variation of parameters. Generally, we write a second order differential equation as y'' + p(x)y' + q(x)y = f(x), where p(x), q(x), and f(x) are functions of x. which indicates the second order derivative of the function. It includes terms like y'', d 2y/dx 2, y''(x), etc. Second order differential equation is a specific type of differential equation that consists of a derivative of a function of order 2 and no other higher-order derivative of the function appears in the equation.
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