## Math Problem Statement

The solution of the equation (27xy² + 8y³)dx + (18x²y + 12xy²)dy = 0 is ψ(x,y) = k. If y(1) = 2 then k = ? Group of answer choices

36

13

68

72

None of the other answers

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Differential Equations

Exact Equations

Integration

### Formulas

∂M/∂y = ∂N/∂x (Exact Differential Equation Condition)

ψ(x, y) = ∫ M(x, y) dx

ψ(x, y) = k with initial conditions y(1) = 2

### Theorems

Exact Differential Equation Theorem

### Suitable Grade Level

Undergraduate Calculus

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