The order and degree of the differential equation 3- ( d ^3 y d x^3 )^ 7 3 = ( dy d x )^5 are respectively

Step-by-step solution

To determine the order and degree of the differential equation 3- ( d ³ y d x³ )^ 7 3 = ( d y d x )⁵ , we identify the highest order derivative present. The equation contains d ³ y d x³ and d y d x , making the order 3 . To establish the degree, we isolate the radical term and eliminate fractional exponents by raising both sides to the power of 3 : [ ( d ³ y d x³ )^ 7 3 ]³ = [3 - ( d y d x )⁵ ]³ Thus, ( d ³ y d x³ )⁷ = [3 - ( d y d x )⁵ ]³ . The highest power of the highest order derivative is 7 , so the degree is