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Determine the order and degree of the following differential equation: dydxdydx(dydx)23=d2ydx2 - Mathematics and Statistics

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Sum

Determine the order and degree of the following differential equation:

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`

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Solution

The given D.E. is

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`

On cubing both sides, we get

`1 +("dy"/"dx")^2 = (("d"^2"y")/"dx"^2)^3`

This D.E. has highest order derivative `("d"^2"y")/"dx"^2` with power 3.

∴ the given D.E. is of order 2 and degree 3.

Concept: Order and Degree of a Differential Equation
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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 2 | Q 1.3 | Page 216
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