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Question
Write the order and degree of the differential equation `((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`.
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Solution
Since,
The given differential equation is
`((d^4"y")/(d"x"^4))^2 = [ "x" + ((d"y")/(d"x"))^2]^3`
`((d^4"y")/(d"x"^4))^2 = "x"^3 + ((d"y")/(d"x"))^6 + 3"x"^2 ((d"y")/(d"x"))^2 + 3"x" ((d"y")/(d"x"))^4`
The highest order derivative in the differential equation is `(d^4"y")/(d"x"^4)` ⇒ Order of the given differential equation is 4.
The highest power raised to `(d^4"y")/(d"x"^4)` is 2⇒ Degree of the given differential equation is 2.
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