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

Step-by-step solution

The given differential equation is 2 + ( d^2 y dx^2 )^3 = ( d^3 y dx^3 )^ 5/2 Squaring both sides to remove fractional powers, we get: 2 + ( d^2 y dx^2 )^3 = ( d^3 y dx^3 )^5 The highest order derivative present in the equation is d^3 y dx^3 , so the order of the differential equation is 3 . The power of the highest order derivative is 5 , so the degree of the differential equation is 5 . Therefore, the order and degree are 3 and 5 respectively. Answer: 3, 5