Consider the differential equation with the initial condition

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Consider the differential equation dydx=y2−x\dfrac{dy}{dx}=y^{2}-x with the initial condition y(1)=1y(1)=1. Using two equal horizontal steps of size Δx=0.4\Delta x=0.4, successively follow the directions indicated by the slope field to approximate the value of yy when x=1.8x=1.8.

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