Consider the differential equation with initial condition .
MATHEMATICS · Multi-part · AP · Calculus BC · Differential Equations · Differential Equations
Problem
Consider the differential equation dxdy=2x+21y with initial condition y(0)=2.
(a) Beginning at (0,2), follow the slope segments as straight lines of horizontal length Δx=0.25 to approximate the solution’s y-value at x=1. Present your work in a table that shows, for each step, the point used, the slope at that point, and the resulting estimate for the next y-value.
(b) Solve the differential equation analytically and use the exact solution to determine the true value of y(1).
(c) Calculate the absolute error in your graphical approximation from part (a). Interpret the sign and magnitude of this error in the context of the slope field.