u(x,t)=\frac{t}{2}+\sum_{n=1}^{\infty}\cos\!\bigl(\tfrac{n\pi x}{L}\bigr)\bigl[a_{n}\cos\!\bigl(\tfrac{n\pi a t}{L}\bigr)+b_{n}\sin\!\bigl(\tfrac{n\pi a t}{L}\bigr)\bigr],
u(x,t)=\frac{a_{0}}{2}+\frac{b_{0}}{2}\,t+\sum_{n=1}^{\infty}\cos\!\bigl(\tfrac{n\pi x}{L}\bigr) \bigl[a_{n}\cos\!\bigl(\tfrac{n\pi a t}{L}\bigr)+b_{n}\sin\!\bigl(\tfrac{n\pi a t}{L}\bigr)\bigr].
Passo 2
Comparemos o termo de ordem zero em x e t na solução dada: