A second-order differential equation is a mathematical equation that involves an unknown function, its first derivative, and its second derivative.
In other words, a second-order differential equation takes the form:
d^2y/dx^2 = f(x, y, dy/dx)
where y is the unknown function, x is the independent variable, dy/dx is the first derivative of y with respect to x, and f(x, y, dy/dx) is some function that depends on x, y, and dy/dx.
Second-order differential equations are often used to model physical phenomena, such as the motion of objects under the influence of forces or the behavior of electrical circuits. They are also important in many branches of mathematics and engineering.
Solving a second-order differential equation involves finding a function that satisfies the equation. This is typically done by using techniques such as separation of variables, variation of parameters, or Laplace transforms.