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A second order differential equation form d2y/dx2 = f(x,y,dx/dy)
How do I read the language on the right hand side?
How do I read the language on the right hand side?
The righthand side is some function of x, y, and dy/dx. For example, it could be x2y - 3dy/dx.negation said:A second order differential equation form d2y/dx2 = f(x,y,dx/dy)
How do I read the language on the right hand side?
Mark44 said:The righthand side is some function of x, y, and dy/dx. For example, it could be x2y - 3dy/dx.
A second order differential equation is a mathematical equation that involves the second derivative of a function. It is used to describe the behavior of physical systems and can be solved to determine the function that satisfies the equation.
The general form of a second order differential equation is d2y/dx2 = f(x,y,dy/dx), where y is the dependent variable, x is the independent variable, and f is a function that relates these variables. This form is also known as the standard form.
The two types of second order differential equations are homogeneous and non-homogeneous. Homogeneous equations have a right-hand side that is equal to 0, while non-homogeneous equations have a non-zero right-hand side.
There are various methods for solving second order differential equations, including separation of variables, variation of parameters, and using integrating factors. The specific method used depends on the form of the equation and the initial conditions given.
Second order differential equations are used in many areas of science and engineering to model physical systems such as motion, heat transfer, and electrical circuits. They are also used in economics, biology, and chemistry to analyze and predict behavior and changes in systems.