Differential Equations (id: f783659d8)

本题目来源于试卷: Differential Equations，类别为 IB数学

[问答题]
1. Show that $y=\frac{1}{2x^2}\int f(x)\mathrm{d}x$ is a solution of the differential equation

$2x^2\frac{\mathrm{d}y}{\mathrm{d}x}+4xy=f(x)$ .

2. Hence solve $2x^2\frac{\mathrm{d}y}{\mathrm{d}x}+4xy=\frac{1}{x}$, x>0 , given that y=2 when x=1 .

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