sil = NDSolve[{D[u[t, x], {t, 2}] == D[u[t, x], {x, 2}],
u[0, x] == Exp[-(x^2)], u[t, -10] == u[t, 10],
D[u[t, x], t = 0] == 0}, u, {t, 0, 40}, {x, -10, 10}]
{u, t, x} = {u, t, x} /. sil[[1]]
Manipulate[Plot[u[t, x], {x, -10, 10}], {t, 0, 40, 0.1}]

顺便问一下这两个图像有可能整合到一个图像里去吗，用Manipulate命令，可调的是x与t的值
sil = NDSolve[{D[u[t, x], t] == D[u[t, x], {x, 2}], u[0, x] == 0,
u[t, 0] == Sin[t], u[t, 5] == 0}, u, {t, 0, 10}, {x, 0, 5}]
{u, t, x} = {u, t, x} /. sil[[1]]
Manipulate[Plot[u[t, x], {t, 0, 10}], {x, 0, 5, 0.1}]

没有D[f[t],t=0]这种用法。应为Derivative[1][f][0]

是题目，镇楼是第三题，二楼是第二题