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Question
The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.
Options
Straight lines
Circles
Parabolas
Ellipses
Solution
The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of parabolas.
Explanation:
Given equation can be written as `(2"d"y)/(y + 3) = "dx"/x`
⇒ 2log (y + 3) = logx + logc
⇒ (y + 3)2 = cx which represents the family of parabolas.
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