求解微分方程,麻烦给出过程。

2025-05-20 12:21:52
推荐回答(1个)
回答1:

dy/dx = (y-x^3)/(2x) = y/(2x) - x^2/2
y' - y/(2x) = -x^2/2 是一阶线性微分方程,
y = e^[∫dx/(2x)] {∫(-x^2/2)e^[∫-dx/(2x)]dx + C}
= √x [-(1/2)∫x^(3/2)dx + C]
= √x [-(1/5)x^(5/2) + C] = -(1/5)x^3 + C√x