本题目来源于试卷: Differential Equations，类别为 IB数学
[问答题]
Consider the differential equam7hac/.gm d9cgux6 w vp0):i4fi b +jxl+*ihtqs)mvnr023secw d/ +q tion $ \frac{\mathrm{d} y}{\mathrm{~d} x}-(\tan x) y=1$ , where $x \neq \frac{(2 n+1) \pi}{2} $, for any integer n .
1. Given that y(0)=1 , use Euler's method with step length h=0.2 to find an approximation for y(1) . Give your answer correct to two decimal places.
2. Solve the equation $ \frac{\mathrm{d} y}{\mathrm{~d} x}-(\tan x) y=1 $. Give your answer in the form y=f(x) .
3. Find the percentage error when y(1) is approximated by the final rounded value found in part (a). Give your answer correct to two significant figures.
4. Show that the x -coordinate(s) of the points on the curve y=f(x) where $ \frac{\mathrm{d} y}{\mathrm{~d} x}=0 $ are of the form $x=\frac{1}{2}(4 \pi n-\pi)$ , where $ n \in \mathbb{Z}$ .
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