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3xf'(x) - 8f(x) = 12x^(5/3)
x ≠ 0 时化为，f'(x) - 8f(x)/(3x) = 4x^(2/3)
f(x) = e^(∫8dx/(3x) [C + ∫4x^(2/3)e^(-∫8dx/(3x)dx]
= x^(8/3) [C + 4∫x^(2/3)x^(-8/3)dx]
= x^(8/3) [C + 4∫x^(-2)dx] = x^(8/3) (C - 4/x)
f(-1) = 5代入，得 5 = 1(C +4)， C = 1
f(x) = x^(8/3) (1 - 4/x) = x^(8/3) - 4x^(5/3)
f'(x) = (8/3)x^(5/3) - (20/3)x^(2/3)
f''(x) = (40/9)x^(2/3) - (40/9)x^(-1/3) = (40/9)(x-1)/x^(1/3)
令 f''(x) = 0， 得 x = 1, f''(x) 在 1 左右二阶导数变号，则拐点 (1, -3),
凹区间 x∈(-∞,0)∪(1, +∞) ; 凸区间 x∈(0, 1).
x ≠ 0 时化为，f'(x) - 8f(x)/(3x) = 4x^(2/3)
f(x) = e^(∫8dx/(3x) [C + ∫4x^(2/3)e^(-∫8dx/(3x)dx]
= x^(8/3) [C + 4∫x^(2/3)x^(-8/3)dx]
= x^(8/3) [C + 4∫x^(-2)dx] = x^(8/3) (C - 4/x)
f(-1) = 5代入，得 5 = 1(C +4)， C = 1
f(x) = x^(8/3) (1 - 4/x) = x^(8/3) - 4x^(5/3)
f'(x) = (8/3)x^(5/3) - (20/3)x^(2/3)
f''(x) = (40/9)x^(2/3) - (40/9)x^(-1/3) = (40/9)(x-1)/x^(1/3)
令 f''(x) = 0， 得 x = 1, f''(x) 在 1 左右二阶导数变号，则拐点 (1, -3),
凹区间 x∈(-∞,0)∪(1, +∞) ; 凸区间 x∈(0, 1).
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