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dy xy . dx 2 a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. 1998 BC4 Consider the differential equation y x b) Given the initial condition, f(0)=2, sketch the solution curve on the axes above. Use your solution to estimate f(1). c) Find the particular solution y=f(x) to the given differential equation with the initial condition f(0)=2. Use your solution to find f(1). 1998 AB4 Let f be a function with f(1) = 4 such that for all points (x,y) on the graph of f the slope is given by 3x 2 1 . 2y a) Find the slope of the graph of f at the point where x = 1. b) Write an equation for the line tangent to the graph of f at x =1 and use it to approximate f(1.2) dy 3x 2 1 dx 2y c) Find f(x) by solving the differential equation d) Use your solution from part (c) to find f(1.2). 1. ò 2 1 3dx (3x - 2) 2 2. ò 3 2 4xe4 x -5 dx = 2