(9/1/08)Math 10B. Lecture Examples.Section 11.3. Euler’s method†Example 1 Figure 1 shows the slope field for the differential equation,dydx= (1 − x)y.Draw the graph of approximate solution y = yE(x) for 0 ≤ x ≤ 4 with the initial valuey(0) = 1 that is obtained by Euler’s method with the partition, 0 < 1 < 2 < 3 < 4.x1 2 3 4y12Slope field fordydx= (1 − x)yFIGURE 1Answer: Figure A1a • (Figure A1b shows the graph of the exact solution y = y(x) with the Euler approximation.)x1 2 3 4y12x1 2 3 4y12Figure A1a Figure A1b†Lecture notes to accompany Section 11.3 of Calculus by Hughes-Hallett et al.1Math 10B. Lecture Examples. (9/1/08) Section 11.3, p. 2Example 2 Use Euler’s method with four subintervals to find the values at the partition points ofan approximate solution ofdydx=(1 − x)yx, y(1) = 3, 1 ≤ x ≤ 5. Then draw its graphAnswer: yE(1) = 3 • yE(2) = 1.5 • yE(4) = 0.5 • yE(5) = 0.125 • Figure A2x1 2 3 4 5y123Figure A2Interactive ExamplesWork the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡Section 9.4: Example 1‡The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sectionsof the textbook for the