Answer to Question #297055 in Differential Equations for Prince

Question

<e> A uniform string of line density rho stretched to tension rho.a^2 ,executes small transverse vibration in a plane through the undisturbed line of the string. the ends x=0 ; x= l of the string are fixed . Point x=b drawn aside through a small distance d and released at time t=0. Find the transverse displacement of any point of the string at any subsequent time.