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Question
Find the order and degree of the following differential equation:
`(("d"y)/("d"x))^3 + y = x - ("d"x)/("d"y)`
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Solution
`(("d"y)/("d"x))^3 + y = x - [1/((("d"x)/("d"y)))]`
`(("d"y)/("d"x))^3 + y = [(x(("d"y)/("d"x)) - 1)/((("d"y)/("d"x)))]`
`("d"y)/("d"x) [(("d"y)/("d"x))^3 + y] = x(("d"y)/("d"x)) - 1`
`(("d"y)/("d"))^4 + y(("d"y)/("d"x)) = x(("d"y)/("d"x)) - 1`
Highest order derivative is `("d"y)/("d"x)`
∴ Order = 1
Power of the highest order derivative `("d"y)/("d"x)` is 4
∴ Degree = 4
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