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Question
Determine the order and degree of the following differential equation:
`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`
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Solution
The given D.E. is
`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`
On squaring both sides, we get
`("x" + ("d"^2"y")/"dx"^2)^2 = 1 + (("d"^2"y")/"dx"^2)^2`
∴ `"x"^2 + "2x" ("d"^2"y")/"dx"^2 + (("d"^2"y")/"dx"^2)^2 = 1 + (("d"^2"y")/"dx"^2)^2`
∴ `"x"^2 + "2x" ("d"^2"y")/"dx"^2 - 1 = 0`
This D.E. has highest order derivative `("d"^2"y")/"dx"^2` with power 1.
∴ the given D.E. has order 2 and degree 1.
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