Consider the equation u t
​
=4(u rr
​
+ r
1
​
u r
​
),00, with the boundary condition u(1,t)=0,t>0, and the initial condition u(r,0)=3,0 [infinity]
​
a m
​
J 0
​
(α m
​
r)e −4α m
2
​
t
where the coefficient a m
​
= α m
​
J 1
​
(α m
​
)
k
​
, find the value of k. a) 4 b) 6 c) −2 d) 8 e) 10 f) −12