Page 1 of 1
(a) A unifom rod of length 10 meters is held at both ends. The initial temperature at any point on the rod is f(x). The
Posted: Tue Jul 12, 2022 12:46 pm
by answerhappygod
- A A Unifom Rod Of Length 10 Meters Is Held At Both Ends The Initial Temperature At Any Point On The Rod Is F X The 1 (40.22 KiB) Viewed 41 times
(a) A unifom rod of length 10 meters is held at both ends. The initial temperature at any point on the rod is f(x). The temperature at both ends is held fixed at a constant temperature of 0∘C. The temperature u(x,t) at any time t of a point P which is x distance away from any of the two endpoints is ∂t∂u=4∂x2∂2u,(0<x<10,t>0), i. Use the method of separation of variables to show that the general solution is given by u(x,t)=(Acosλx+Bsinλx)e−4λ2t. such that A,B and λ are constant.