The degree of the differential equation [1+ ( d y d x )^2 ]^ 3 4 = ( d^2 y d x^2 )^ 1 3

Step-by-step solution

The given differential equation is [1 + ( dy dx )^2 ]^ 3 4 = ( d^2y dx^2 )^ 1 3 . To eliminate the fractional exponents, raise both sides to the power of 12 , which is the least common multiple of the denominators 4 and 3 . ( [1 + ( dy dx )^2 ]^ 3 4 )¹² = ( ( d^2y dx^2 )^ 1 3 )¹² Simplifying the exponents: [1 + ( dy dx )^2 ]⁹ = ( d^2y dx^2 )⁴ The highest order derivative present in the equation is d^2y dx^2 , which is of order 2 . The degree of a differential equation is the power of the highest order derivative wh