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求微分方程dy/dx-y/x=3x满足初始条件y|(x=1 ) =4的特解,
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dy/dx-y/x = 3x 为一阶线性微分方程, 通解是
y = e^(∫dx/x)[∫3xe^(-∫dx/x)dx + C]
= x[∫3dx + C] = x(3x + C)
x = 1, y = 4 代入得 C = 1, 则特解是 y = 3x^2 + x
y = e^(∫dx/x)[∫3xe^(-∫dx/x)dx + C]
= x[∫3dx + C] = x(3x + C)
x = 1, y = 4 代入得 C = 1, 则特解是 y = 3x^2 + x
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