= Solution
\b[One scalar initial condition is needed in each case], because each equation is first order and each regular solution has one integration constant. The usual <Picard-Lindelöf theorem> applies locally at a regular initial point. For part (c), this requires $x_0\ne0$ and $y_0\ne0$; a condition at an excluded singular endpoint cannot specify a classical solution there. Arbitrary distant boundary data also need not be compatible with one common <interval> of existence.
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