Q-2 - Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°C. At t=0, the rod is taken out and...

Extracted text: Q-2 - Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°C. At t=0, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t), where x is the distance from the left end of the rod, x=0. The U(xt) is a solution of the initial boundary value problem: U, = x Uxx x = 1.14 With boundary conditions as U(0, t) = U(50,t) = 0 30, 0< 25="" initial="" condition:="" u(x,0)="lo," 25="">< x="">< 50="" find="" the="" solution="" u(x,t)="" of="" the="" given="">