# 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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