Solve the boundary value problem of the wave equation ∂t 2
∂ 2
u
​
= π 2
1
​
∂x 2
∂ 2
u
​
for 00 subject to the conditions u(0,t)=u(1,t)=0 for t>0,
u(x,0)=1−x,0 ​
(x,0)=0 for 0 ​