The order and degree of the differential equation ( dy dx )^2 + dx dy = x is:

Step-by-step solution

The given differential equation is ( dy dx )^2 + dx dy = x . We know that dx dy = 1 dy dx . Substituting this in the given equation, we get: ( dy dx )^2 + 1 dy dx = x Multiplying both sides by dy dx , we get: ( dy dx )^3 + 1 = x dy dx ( dy dx )^3 - x dy dx + 1 = 0 The highest order derivative present in the equation is dy dx , so the order is 1 . The highest power of the highest order derivative is 3 , so the degree is 3 . Thus, the order and degree are (1, 3) . Answer: (1, 3)