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Choose the correct option from the given alternatives: x2 + y2 = a2 is a solution of - Mathematics and Statistics

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MCQ

Choose the correct option from the given alternatives:

x2 + y2 = a2 is a solution of

Options

  • `("d"^2"y")/"dx"^2 + "dy"/"dx" - "y" = 0`

  • y = x`sqrt(1 + ("dy"/"dx")^2) + "a"^2 "y"`

  • y = x`"dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`

  • `("d"^2"y")/"dx"^2 = ("x + 1")"dy"/"dx"`

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Solution

y = x`"dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`

Hint:

x2 + y2 = a    ∴ 2x + 2y`"dy"/"dx" = 0`

∴ `"dy"/"dx" = - "x"/"y"`

∴ `"x" "dy"/"dx" + "a" sqrt(1 + ("dy"/"dx")^2)`

`= "x"(- "x"/"y") + "a"sqrt(1 + "x"^2/"y"^2) = - "x"^2/"y" + "a" xx "a"/"y"`

`= ("a"^2 - "x"^2)/"y" = "y"^2/"y" = "y"`

Concept: Formation of Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Differential Equations
Miscellaneous exercise 1 | Q 1.03 | Page 215
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