TannY said:thanx! ^^
i thought that (e^2x)squared = (e^4x) lol
A second order differential equation is a mathematical equation that involves the second derivative of a function. This means that the equation relates the rate of change of a quantity to its acceleration or curvature.
Proving second order differential equations helps us understand and predict the behavior of many natural and physical phenomena, such as motion, heat transfer, and electrical circuits. It also allows us to solve complex mathematical problems and make accurate predictions about the future behavior of a system.
To prove a second order differential equation, you need to show that the equation holds true for all possible values of the variables involved, using mathematical methods such as substitution, integration, and differentiation. This involves demonstrating that both sides of the equation are equal for all values of the variables.
Second order differential equations are used in a wide range of fields, including physics, engineering, economics, and biology. They are used to model and analyze various phenomena such as population growth, pendulum motion, electrical circuits, and chemical reactions.
Linear second order differential equations have a linear relationship between the dependent variable, its first derivative, and its second derivative. Nonlinear second order differential equations have a nonlinear relationship between these variables, making them more complex and difficult to solve. Linear equations have known solutions, while nonlinear equations often require numerical methods for approximation.