Show that the function u = u ( x , t ) is a solution of the wave equation u t t = a 2 u x x . (a) u = sin ( k x ) sin ( a k t ) (b) u = t / a 2 t 2 − x 2 (c) u = ( x − a t ) 6 + ( x + a t ) 6 (d) u = sin ( x − a t ) + ln ( x + a t )
Show that the function u = u ( x , t ) is a solution of the wave equation u t t = a 2 u x x . (a) u = sin ( k x ) sin ( a k t ) (b) u = t / a 2 t 2 − x 2 (c) u = ( x − a t ) 6 + ( x + a t ) 6 (d) u = sin ( x − a t ) + ln ( x + a t )
Solution Summary: The author explains that the function u=u(x,t) is a solution of the wave equation.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY