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Question
Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax
Solution
x2 + y2 = 2ax ......(i)
Here, a is an arbitrary constant.
Differentiating (i) w.r.t. x, we get
`2x + 2y ("d"y)/("d"x)` = 2a
∴ `2x + 2y ("d"y)/("d"x) = (x^2 + y^2)/x` .....[From (i)]
∴ `2x^2 + 2xy ("d"y)/("d"x)` = x2 + y2
∴ `2xy ("d"y)/("d"x)` = y2 − x2
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