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Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax - Mathematics and Statistics

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Sum

Find the differential equation by eliminating arbitrary constants from the relation x2 + y2 = 2ax

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Solution

Given relation is

x2 + y2 = 2ax     .....(i)

Differentiating w.r.t. x, we get

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

Substituting (ii) in (i), we get

x2 + y2 = `(2x+ 2y ("d"y)/("d"x))x`

∴ x2 + y2 = `2x^2+ 2xy ("d"y)/("d"x)`

∴ `2xy ("d"y)/("d"x)` = y2 – x2, which is the required differential equation.

Concept: Formation of Differential Equation by Eliminating Arbitary Constant
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.2 | Q 2 | Page 163
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