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http://functions.wolfram.com/06.38.13.0009.01
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Derivative[3][w][z] + ((2 Derivative[1][g][z])/g[z] -
(3 Derivative[1][h][z])/h[z] - (3 Derivative[2][g][z])/
Derivative[1][g][z]) Derivative[2][w][z] +
(-((4 Derivative[1][g][z] Derivative[1][h][z])/(g[z] h[z])) -
(3 Derivative[2][h][z])/h[z] + (6 Derivative[1][h][z]^2)/h[z]^2 +
Derivative[1][g][z]^2 - (2 Derivative[2][g][z])/g[z] +
(6 Derivative[1][h][z] Derivative[2][g][z])/(h[z] Derivative[1][g][z]) +
(3 Derivative[2][g][z]^2)/Derivative[1][g][z]^2 -
Derivative[3][g][z]/Derivative[1][g][z]) Derivative[1][w][z] +
((2 Derivative[1][h][z] Derivative[2][g][z] - 2 Derivative[1][g][z]
Derivative[2][h][z])/(h[z] g[z]) -
(Derivative[1][g][z]^2 Derivative[1][h][z] + Derivative[3][h][z])/h[z] +
(4 Derivative[1][g][z] Derivative[1][h][z]^2)/(g[z] h[z]^2) +
(6 Derivative[1][h][z] Derivative[2][h][z])/h[z]^2 -
(6 Derivative[1][h][z]^3)/h[z]^3 -
(6 Derivative[1][h][z]^2 Derivative[2][g][z])/
(h[z]^2 Derivative[1][g][z]) - (3 Derivative[1][h][z]
Derivative[2][g][z]^2)/(h[z] Derivative[1][g][z]^2) +
(3 Derivative[2][g][z] Derivative[2][h][z] + Derivative[1][h][z]
Derivative[3][g][z])/(h[z] Derivative[1][g][z])) w[z] == 0 /;
w[z] == Subscript[c, 1] h[z] CosIntegral[g[z]] +
Subscript[c, 2] h[z] SinIntegral[g[z]] + Subscript[c, 3] h[z]
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