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Sum

Find the differential equation by eliminating arbitrary constants from the relation x^{2} + y^{2 }= 2ax

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#### Solution

Given relation is

x^{2 }+ y^{2} = 2ax .....(i)

Differentiating w.r.t. x, we get

`2x + 2y ("d"y)/("d"x)` = 2a ......(ii)

Substituting (ii) in (i), we get

x^{2 }+ y^{2} = `(2x+ 2y ("d"y)/("d"x))x`

∴ x^{2 }+ y^{2} = `2x^2+ 2xy ("d"y)/("d"x)`

∴ `2xy ("d"y)/("d"x)` = y^{2} – x^{2}, which is the required differential equation.

Concept: Formation of Differential Equation by Eliminating Arbitary Constant

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