The unique solution for the differential equation xy = y exists on the region ______?
- Half planes defined by either x > 0 or x < 0
- The vertical axis x = 0
- The horizontal axis y = 0
- None of these
Explanation
The differential equation xy' = y can be rewritten as y'/y = 1/x.
This equation has a unique solution when x ≠ 0, since dividing by zero is undefined.
The solution exists on the region defined by either x > 0 or x < 0.
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