A calculus problem by Rocco Dalto

Calculus Level 5

The solution to the differential \( x^2 \dfrac{d^2y}{dx^2} - x \dfrac{dy}{dx} + 2y = 0 \), where \( y(1) = \dfrac{3}{2}\), \(y'(1) = 2 \) can be expressed as the the curve \( y = f(x)\).

The area of the above curve \( y = f(x) \) from \( x = 1 \) to \( x = e^{2\pi} \) can be expressed as \(\dfrac{a}{b} * (e^{c\pi} - a) \), where \(a\), \(b\), and \(c\) are coprime positive integers.

Find: \(a + b + c. \) \(\)

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