The sum of the order and degree of the differential equation ( d^2 y d x^2 )^5+ 4 ( d^2 y d x^2 )^3 ( d^3 y d x^3 ) + d^3 y d x^3 =x^2-1 is

Step-by-step solution

The given differential equation is ( d^2 y d x^2 )^5 + 4 ( d^2 y d x^2 )^3 ( d^3 y d x^3 ) + d^3 y d x^3 = x^2 - 1 . To determine the order and degree, the equation must be expressed as a polynomial in terms of the derivatives. Multiplying the entire equation by d^3 y d x^3 to eliminate the denominator, we get: ( d^2 y d x^2 )^5 ( d^3 y d x^3 ) + 4 ( d^2 y d x^3 )^3 + ( d^3 y d x^3 )^2 = (x^2 - 1) ( d^3 y d x^3 ) . The highest order derivative present in the equation is d^3 y d x^3 , so the order of the differentia