Find the Value of K Such That the Differential Equation $\left( x y ^ { 2 } + k x ^ { 5 } y + x ^ { 4 } \right) d x + \left( x ^ { 6 } + x ^ { 2 } y + y ^ { 6 } \right) d y = 0$

Multiple Choice

Find the value of k such that the differential equation $\left( x y ^ { 2 } + k x ^ { 5 } y + x ^ { 4 } \right) d x + \left( x ^ { 6 } + x ^ { 2 } y + y ^ { 6 } \right) d y = 0$ is exact.

A) 5
B) 4
C) 8
D) 7
E) 6