Answers to the differential equation dy/dx = xy^3 additionally satisfy d^2y/dx^2 = y^3 (1 + 3x^2 y^2). Allow y = f(x) be a certain way to this differential equation with f(1) = 2 compose an equation the line tangent on graph of y = f(x) at x = 1. Make use of the tangent line equation from component (a) to approximate f (1.1). Discover the specific way to this differential equation with initial condition f(1) = 2.

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