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Question
Determine the order and degree of the following differential equation:
`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`
Solution
The given D.E. is
`(("d"^3"y")/"dx"^3)^2 = root(5)(1 + "dy"/"dx")`
`(("d"^3"y")/"dx"^3)^(2xx5) = 1 + "dy"/"dx"`
`(("d"^3"y")/"dx"^3)^10 = 1 + "dy"/"dx"`
This D.E. has highest order derivative `("d"^3"y")/"dx"^3` with power 10.
∴ the given D.E. is of order 3 and degree 10.
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