Sum of the squares of the order and degree (if defined) of a differential equation 2 y^ + (y^ )^2= y^ -3 is

Step-by-step solution

Given differential equation is 2 y^ + (y^ )^2 = y^ - 3 To find the degree, we must express the differential equation as a polynomial in its derivatives. Squaring both sides, we get: (2 y^ + (y^ )^2)^2 = y^ - 3 4 (y^ )^2 + 4 y^ (y^ )^2 + (y^ )^4 = y^ - 3 (y^ )^4 + 4 y^ (y^ )^2 - y^ + 4 (y^ )^2 + 3 = 0 The highest order derivative present in the equation is y^ , so the order is 2 . The highest power of the highest order derivative y^ is 4 , so the degree is 4 . Sum of the squares of the order and degree is 2^2 + 4^2