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Question
Determine the order and degree of the following differential equation:
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
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Solution
The given D.E. is
`("d"^2"y")/"dx"^2 + "dy"/"dx" + "x" = sqrt(1 + ("d"^3"y")/"dx"^3)`
On squaring both sides, we get
`(("d"^2"y")/"dx"^2 + "dy"/"dx" + "x")^2 = 1 + ("d"^3"y")/"dx"^3`
This D.E. has highest order derivative `("d"^3"y")/"dx"^3` with power 1.
∴ the given D.E. has order 3 and degree 1.
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