本题目来源于试卷: Differential Equations，类别为 IB数学
[问答题]
1. Consider the differential eq *qy :h2bmob pwlcf gxrk0i6;y9f.4g*uati; .m l)xpcamyob .vg,g3l: -(mps w1ubon
$\frac{\mathrm{d} y}{\mathrm{~d} x}=f\left(\frac{y}{x}\right), \quad x\lt 0$ .
Use the substitution$ v=\frac{y}{x}$ to show that the general solution of this differential equation is
$\int \frac{\mathrm{d} v}{f(v)-v}=\ln x+C$
2. Hence, or otherwise, solve the differential equation
$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{4 x^{2}+5 x y+y^{2}}{x^{2}}, \quad x\lt 0$,
given that y=2 when x=1 . Give your answer in the form y=g(x) .
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