本题目来源于试卷: Differential Equations，类别为 IB数学
[问答题]
The curves y=f(x) and y=g(x) bothmcnl8qa.i xel 0y(kw*p2 kvb5u+..a dvu*wj8 pass through t4e 7x7cmbywex e;f5,khe point (1,0) and are defined by the differential equat cwx4x7m5e kbee f,7y;ions $ \frac{\mathrm{d} y}{\mathrm{~d} x}=2 x-y^{2}$ and $\frac{\mathrm{d} y}{\mathrm{~d} x}=3 y-\frac{x}{2} $ respectively.
1. Show that the tangent to the curve y=f(x) at the point (1,0) is normal to the curve y=g(x) at the point (1,0) .
2. Find g(x) .
3. Use Euler's method with steps of 0.2 to estimate f(2) to 5 decimal places.
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