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题中微分方程即 f' - f/x = 3x/2 是一阶线性微分方程，则
f(x) = e^(∫dx/x) [∫(3x/2)e^(-∫dx/x)dx + C]
= x [∫(3/2)dx + C] = (3/2)x^2 + Cx, 过原点 O，
S = ∫<0, 1> [(3/2)x^2 + Cx]dx = [(1/2)x^3+(C/2)x^2]<0, 1>
= 1/2+C/2 = 3, C = 5,
f(x) = (3/2)x^2 + 5x
V = π∫<0, 1> [(3/2)x^2 + 5x]^2 dx
= π∫<0, 1> [(9/4)x^4+15x^3+25x^2] dx
= π[(9/20)x^5 +(15/4)x^4+(25/3)x^3]<0, 1> = 188π/15
f(x) = e^(∫dx/x) [∫(3x/2)e^(-∫dx/x)dx + C]
= x [∫(3/2)dx + C] = (3/2)x^2 + Cx, 过原点 O，
S = ∫<0, 1> [(3/2)x^2 + Cx]dx = [(1/2)x^3+(C/2)x^2]<0, 1>
= 1/2+C/2 = 3, C = 5,
f(x) = (3/2)x^2 + 5x
V = π∫<0, 1> [(3/2)x^2 + 5x]^2 dx
= π∫<0, 1> [(9/4)x^4+15x^3+25x^2] dx
= π[(9/20)x^5 +(15/4)x^4+(25/3)x^3]<0, 1> = 188π/15
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