show that the fuction y(x,t)=x^2+v^2t^s is a solution to the wave equation ? Sol
ID: 2217640 • Letter: S
Question
show that the fuction y(x,t)=x^2+v^2t^s is a solution to the wave equation ?Explanation / Answer
dy/dx = 2x d2y/dx2= 2 ==> I . dy/dt= 2v^2t d2y/dt2= 2v^2 ==>II . plug them exactly like they are in the wave equation d^2 y / dx^2 = (1/V^2 ) d^2 y/ dt^2. plug I and II in the wave equation : and ask is the left side equals the right side of the equation !!? is 2 = 1/V^2 x 2v^2 >> which v^2 cancels with v^2 and this will end with 2=2 and this is correct so its the solution to the wave equation !! . if you ended up with something not correct like 2=3 means its not the solution , Got it ? :) Hope this helps
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.