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

question 36

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

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