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Choose the correct option from the given alternatives: xaybx2a2-y2b2=1 is a solution of - Mathematics and Statistics

MCQ

Choose the correct option from the given alternatives:

`"x"^2/"a"^2 - "y"^2/"b"^2 = 1` is a solution of

Options

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

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

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

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

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Solution

`"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`

Hint: 

`"x"^2/"a"^2 - "y"^2/"b"^2 = 1`      .....(1)

∴ `1/"a"^2 xx "2x" - 1/"b"^2 xx "2y" "dy"/"dx" = 0`

∴ `"x"/"a"^2 - "y"/"b"^2 "dy"/"dx" = 0`    ....(2)

and `1/"a"^2 xx 1 - 1/"b"^2 ["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2] = 0`   ....(3)

Equations (1), (2) and (3) are consistent

∴ `|("x"^2, - "y"^2, 1),("x", -"y" "dy"/"dx", 0),(1, -["y" ("d"^2"y")/"dx"^2 + ("dy"/"dx")^2], 0)| = 0`

∴ `"xy"*("d"^2"y")/"dx"^2 + "x"("dy"/"dx")^2 - "y" "dy"/"dx" = 0`

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 6 | Q 1.13 | Page 216
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