Mathematics · Differential Equations & Conic Sections
Consider the differential equation sin(y/x) (dy/dx + 1) = (y/x) sin(y/x), with initial condition y(1) = π/2, and let α = cos(y(e12) / e12). Let r be the radius of the circle x2 + y2 - 2px + 2py + α + 2 = 0 (where α ≤ 6). Find the number of integral values of 'p'.
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