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In this section, we explore Euler's Method for estimating solutions to first-order differential equations given an initial condition. We focus on the equation y' = x + y, using specified step sizes (dx) to compute approximate values of y at certain x values. The examples illustrate how to apply the method for various initial conditions and step sizes, including cases where calculations are required and where approximations can be made without a calculator. Various scenarios are provided to practice and refine the application of this numerical technique.
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Calculator Required Consider the differential equation y’ = x + y. Use Euler’s method With dx = 0.1 to estimate y when x = 0.4 if: a) y(0) = 1
Calculator Required Given y’ = x + y through (1, 0) and dx = 0.2, find y when x = 1.8
Calculator Required If and y = -2 when x = 3, then find the approximate value of y when x = 3.2 using Euler’s method A. -2.00 B. -2.15 C. -2.20 D. -2.25 E. -2.30
Calculator Required The solution of the differential equation contains the point (3, -2). Using Euler’s method with dx = -0.3 to approximate y when x = 2.7, y = A. -2.98 B. -3.00 C. -3.08 D. -3.25 E. -3.35
No Calculator A. 2.1 B. 2.3 C. 2.5 D. 2.7 E. 2.9
