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Question
Find the order and degree of the following differential equation:
`("d"^2y)/("d"x^2) + y + (("d"y)/("d"x) - ("d"^3y)/("d"x^3))^(3/2)` = 0
Solution
`("d"^2y)/("d"x^2) + y = - (("d"y)/("d"x) - ("d"^3y)/("d"x^3))^(3/2)`
Squaring on both sides
`(("d"^2y)/("d"x^2) + y)^2 = {-(("d"y)/("d"x) - ("d"^3y)/("d"x^3))^(3/2)}`
`(("d"^2y)/("d"x^2) + y)^2 = (("d"y)/("d"x) - ("d"^3y)/("d"x^3))^3`
Highest order derivative is `("d"^3y)/("d"x^3)`
∴ Order = 3
Power of the highest order derivative `("d"^3y)/("d"x^3)` is 3
∴ Degree = 3
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