The Differential Equation $\left( y ^ { 3 } + 6 x y ^ { 4 } \right) d x + \left( 3 x y ^ { 2 } + 12 x ^ { 2 } y ^ { 3 } \right) d y = 0$

question 30

Multiple Choice

The differential equation $\left( y ^ { 3 } + 6 x y ^ { 4 } \right) d x + \left( 3 x y ^ { 2 } + 12 x ^ { 2 } y ^ { 3 } \right) d y = 0$ is

• A) exact with solution \(y ^ { 4 } / 4 + 6 x y ^ { 5 } / 5 + 3 x ^ { 2 } y ^ { 2 } / 2 + 4 x ^ { 3 } y ^ { 3 } + c\)
• B) exact with solution \(y ^ { 4 } / 4 + 6 x y ^ { 5 } / 5 + 3 x ^ { 2 } y ^ { 2 } / 2 + 4 x ^ { 3 } y ^ { 3 } = c\)
• C) exact with solution \(x y ^ { 3 } + 3 x ^ { 2 } y ^ { 4 } = c\)
• D) exact with solution \(x y ^ { 3 } + 3 x ^ { 2 } y ^ { 4 } + c\)
• E) not exact

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