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Question
Determine the order and degree of the following differential equation:
`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`
Solution
`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`
`(("d"^3"y")/"dx"^3)^(1/2) = 20 + ("dy"/"dx")^(1/3)`
Taking power 6 on both sides.
`[(("d"^3"y")/"dx"^3)^(1/2)]^6 = [20 + ("dy"/"dx")^(1/3)]^6`
`(("d"^3"y")/"dx"^3)^3 = [20 + ("dy"/"dx")^(1/3)]^6`
∴ The given differential equation is radical and fraction free and its highest order is 3.
∴ Order = 3, degree = 3
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