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Reduce the following differential equation to the variable separable form and hence solve: x - 2ydydxcos2(x - 2y)=1-2dydx - Mathematics and Statistics

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प्रश्न

Reduce the following differential equation to the variable separable form and hence solve:

`cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"`

बेरीज
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उत्तर

`cos^2 ("x - 2y") = 1 - 2 "dy"/"dx"`      .....(1)

Put x - 2y = u. Then 1 - `2 "dy"/"dx" = "du"/"dx"`

∴ (1) becomes, `cos^2 "u" = "du"/"dx"`

∴ dx = `1/cos^2"u"`du

Integrating both sides, we get

∫ dx = ∫ sec2u du

∴ x = tan u + c

∴ x = tan (x - 2y) + c

This is the general solution.

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Formation of Differential Equations
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पाठ 6: Differential Equations - Exercise 6.3 [पृष्ठ २०१]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
पाठ 6 Differential Equations
Exercise 6.3 | Q 4.4 | पृष्ठ २०१

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