HallsofIvy said:Let y= f(x) be the equation of the mirror. At point [itex](x_0, f(x_0))[/itex], the tangent line to the curve is given by [itex]y= f'(x_0)(x- x_0)+ f(x_0)[/tex]. The line parallel to the x-axis has equation [itex]y= f(x_0)[/itex] and the equation of the line from the origin to the point on the curve has [itex]y= f(x_0)x/x_0[/itex].
To "reflect from the mirror" those two lines must make equal angles with the tangent line.
A 2nd Order ODE (Ordinary Differential Equation) is a mathematical equation that involves an unknown function and its derivatives up to the second order. It is commonly used to model physical phenomena in various fields such as physics, engineering, and economics.
The general method for solving a 2nd Order ODE is by using techniques such as separation of variables, variation of parameters, or the method of undetermined coefficients. The specific method used depends on the form of the equation and the initial conditions given.
The "Mirror for Parallel Reflection from Origin" is a concept used in solving 2nd Order ODEs with boundary conditions that involve the function and its derivatives evaluated at the origin. It involves reflecting the solution of the equation across the origin to obtain a new solution that satisfies the boundary conditions.
Solving 2nd Order ODEs is important because it allows us to model and understand real-world phenomena in a mathematical way. Many physical systems and processes can be described by these equations, making it essential for scientists and engineers to be able to solve them and make predictions.
2nd Order ODEs have a wide range of applications in various fields such as mechanics, electrical circuits, population dynamics, and quantum mechanics. They are used to model and predict the behavior of physical systems, making them essential in scientific research and engineering design.