本题目来源于试卷: Differential Equations，类别为 IB数学
[问答题]
Consider the differential 9cumi4r5 ce+k/ky;uk95pibs x+y6 jffhu8/sy aen*e *(k y1z equation $x \frac{\mathrm{d} y}{\mathrm{~d} x}+y=x^{p+1} $ where $x \in \mathbb{R}$, $x \neq 0 $ and p is a positive integer, p>0 .
1. Solve the differential equation given that y=1 when x=1 . Give your answer in the form y=f(x) .
2. 1. Show that the x -coordinate(s) of the points on the curve y=f(x) where $\frac{\mathrm{d} y}{\mathrm{~d} x}=0 $ satisfy the equation $x^{p+2}=1$ .
2. Deduce the set of values for p such that there are two points on the curve y=f(x) where $ \frac{\mathrm{d} y}{\mathrm{~d} x}=0 $. Give a reason for your answer.
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