The sum of the degree and order of the differential equation d ^2 y d x^2 = [5] dy d x -5 is

Step-by-step solution

The differential equation d ^2 y d x^2 = [5] dy d x -5 contains fractional powers of derivatives. Expressing with exponents: ( d ^2 y d x^2 )^ 1/2 = ( dy d x -5 )^ 1/5 . Raising both sides to the 10th power eliminates the fractional exponents: [ ( d ^2 y d x^2 )^ 1/2 ]¹⁰ = [ ( dy d x -5 )^ 1/5 ]¹⁰ which simplifies to ( d ^2 y d x^2 )^5 = ( dy d x -5 )^2 . The highest derivative is d ^2 y d x^2 of second order, establishing order 2 . The highest power of this derivative is 5, giving degree 5 . The sum is therefore 2