Find the Particular Solution of the Differential Equation $\left( 2 x y - 25 x ^ { 4 } \right) d x + \left( 2 y + x ^ { 2 } + 5 \right) d y = 0$

question 39

Multiple Choice

Find the particular solution of the differential equation $\left( 2 x y - 25 x ^ { 4 } \right) d x + \left( 2 y + x ^ { 2 } + 5 \right) d y = 0$ that satisfies the initial condition $y ( 0 ) = 4$

• A) \(x ^ { 2 } - 25 x ^ { 4 } + 2 y + 5 = 13\)
• B) \(x ^ { 3 } y - 5 x ^ { 4 } + 1 y ^ { 2 } + 5 y = 36\)
• C) \(x ^ { 2 } y - 5 x ^ { 5 } + y ^ { 2 } + 5 y = 36\)
• D) \(x ^ { 2 } - 5 x ^ { 5 } + y ^ { 2 } + 5 = 21\)
• E) \(x ^ { 2 } y - 5 x ^ { 5 } + 2 y ^ { 2 } + 5 = 37\)

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