The order and degree of the differential equation ( d^3 y dx^3 )^ 2 3 - 3 d^2 y dx^2 + 5 dy dx + 4 = 0 are respectively

Step-by-step solution

The given differential equation is ( d^3 y dx^3 )^ 2 3 - 3 d^2 y dx^2 + 5 dy dx + 4 = 0 . The order of a differential equation is the order of the highest derivative present in the equation. The highest derivative is d^3 y dx^3 , so the order is 3 . To find the degree, the differential equation must be expressed as a polynomial in its derivatives. Isolating the term with the fractional power, we get: ( d^3 y dx^3 )^ 2 3 = 3 d^2 y dx^2 - 5 dy dx - 4 Cubing both sides to remove the fractional power, we obtain: ( d^3