Recall that a linear combination/superposition of the functi…
Recall that a linear combination/superposition of the functions v1(x,t), v2(x,t), v3(x,t), …, vn(x,t){“version”:”1.1″,”math”:”v1(x,t), v2(x,t), v3(x,t), …, vn(x,t)”} is a function of the form v ( x , t ) = ∑ k = 1 n α k v k ( x , t ) {“version”:”1.1″,”math”:”v(x,t)=\displaystyle\sum_{k=1}^n\alpha_kv_k(x,t)”}where the αk{“version”:”1.1″,”math”:”αk”} are constants. Find a linear combination/superposition of only the functions you found in question 1 above that are solutions to the heat equation, (i.e., those with a YES), such that this linear combination/superposition satisfies the boundary conditions u ( 0 , t ) = 0 and u x ( 2 , t ) = t , for all t > 0. {“version”:”1.1″,”math”:”u(0,t)=0 \text{ and } u_x(2,t)=t, \text{ for all } t>0.”}If you cannot satisfy these conditions, there is something wrong with your superposition!