Solutions to the differential equation dy/dx = xy^3 also satisfy d^2y/dx^2 = y^3 (1 + 3x^2 y^2). Let y = f(x) be a particular solution to this differential equation with f(1) = 2 write an equation for the line tangent to the graph of y = f(x) at x = 1. Use the tangent line equation from part (a) to approximate f (1.1). Find the particular solution to this differential equation with initial condition f(1) = 2.