DSolve[{h''[x] - (p + w^2)*h[x] == k*cos[w*(y + l)]*DiracDelta[x],
h''[1] == -o*p*h[1], h[-j] == 0}, h[x], x]
{{h[x] -> (1/(
2 (-1 + E^(2 Sqrt[p + w^2] + 2 j Sqrt[p + w^2])) Sqrt[p + w^2]))
E^(-Sqrt[p + w^2] x)
k cos[w (l + y)] (-1 + E^(2 Sqrt[p + w^2]) + E^(
2 j Sqrt[p + w^2] + 2 Sqrt[p + w^2] x) - E^(
2 Sqrt[p + w^2] + 2 j Sqrt[p + w^2] + 2 Sqrt[p + w^2] x) -
E^(2 Sqrt[p + w^2]) HeavisideTheta[-j] +
E^(2 Sqrt[p + w^2] + 2 j Sqrt[p + w^2]) HeavisideTheta[-j] +
E^(2 Sqrt[p + w^2] x) HeavisideTheta[-j] -
E^(2 j Sqrt[p + w^2] + 2 Sqrt[p + w^2] x) HeavisideTheta[-j] +
HeavisideTheta[x] -
E^(2 Sqrt[p + w^2] + 2 j Sqrt[p + w^2]) HeavisideTheta[x] -
E^(2 Sqrt[p + w^2] x) HeavisideTheta[x] +
E^(2 Sqrt[p + w^2] + 2 j Sqrt[p + w^2] + 2 Sqrt[p + w^2] x)
HeavisideTheta[x])}}
Simplify[%1]
{{h[x] -> (
E^(-Sqrt[p + w^2] x)
k cos[w (l +
y)] (-(-1 + E^(2 Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] (j + x))) + (-1 + E^(2 j Sqrt[p + w^2])) (E^(
2 Sqrt[p + w^2]) - E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[-j] + (-1 + E^(
2 (1 + j) Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[x]))/(
2 (-1 + E^(2 (1 + j) Sqrt[p + w^2])) Sqrt[p + w^2])}}
InverseLaplaceTransform[(E^(-Sqrt[p + w^2] x)
k cos[w (l +
y)] (-(-1 + E^(2 Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] (j + x))) + (-1 + E^(2 j Sqrt[p + w^2])) (E^(
2 Sqrt[p + w^2]) - E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[-j] + (-1 + E^(
2 (1 + j) Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[x]))/(2 (-1 + E^(
2 (1 + j) Sqrt[p + w^2])) Sqrt[p + w^2]), p, t]
1/2 k cos[w (l + y)] InverseLaplaceTransform[(
E^(-Sqrt[p + w^2]
x) ((1 - E^(2 Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] (j + x))) + (-1 + E^(2 j Sqrt[p + w^2])) (E^(
2 Sqrt[p + w^2]) - E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[-j] + (-1 + E^(
2 (1 + j) Sqrt[p + w^2])) (-1 + E^(
2 Sqrt[p + w^2] x)) HeavisideTheta[x]))/((-1 + E^(
2 (1 + j) Sqrt[p + w^2])) Sqrt[p + w^2]), p, t]
怎么觉得这个逆变换并没有作用呀？

这里p是拉普拉斯算子，w是finite Fourier cosine transform的算子（不知道这两个有没有影响），x是自变量，h是应变量，其他的都是参数