Math Problem Statement
(2x ^ 2 + xy + y ^ 2) * dx + 2x ^ 2 * dy = 0
Solution
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Math Problem Analysis
Mathematical Concepts
Differential Equations
Exact Equations
Integrating Factor
Substitution
Formulas
M(x, y) * dx + N(x, y) * dy = 0
Partial derivatives: ∂M/∂y = x + 2y, ∂N/∂x = 4x
Condition for exactness: ∂M/∂y = ∂N/∂x
Theorems
Exact Differential Equations Theorem
Integrating Factor Method
Suitable Grade Level
Undergraduate Calculus or Advanced High School
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