# Slope field for the differential equation

**Question description**

dy/dx=xy/2

a) Provide a sketch of the slope field for the differential equation.

b) Let f be the function that satisfies the given differential equation. Write an equation for the tangent line to the curve y=f(x) throughout the point (1,1). Then use that tangent line equation to estimate the value of (1,2).

c) find the particular solution y=f(x) to the differential equation with the initial condition f(1)=1. Use that solution to find f(1,2).

d) Compare your estimate of f (1,2) found in part b to the actual value of f (1,2) found in part c. Was the estimate from part b an underestimate or an overestimate? use the slope field to explain.

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