Question

Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem at the points x = 4.2, 4.4, 4.6, and 4.8. y = {(V2+y),y(4)=1 Complete the table using Euler's method. xn Euler's Method 4.2 4.4 n 1 2 2 3 4.6 4 4.8 (Round to two decimal places as needed.)

Answer 1

when xann Let us consider a first orden, ist dessee differential can equation ou a foring with y(x) = mo Now, yn is the value the Range {xo, an] into sults interval by xo, . ,, or an. #sh, Na 1, 2, "in Now, Sulor firmesion ..is We devide no equal where and ha Ap-l an S fixing are xpl ar xno yolar) - 4(x-1) = s fex,y).sk xrt mo Yo a Ipone & f ( x-1) S are Smee fee, y) = f(-1, 30-1) in kipri kasar Yo ñ Yupon the framan, gori) so, so for Euler egnesson, I= Imagth flan=1, In-1)

dy Now In this pooblem, G45) ay (4)=1 SO Yo = 1, no=4, h = 0-2 feris) - Cy² ) So from() y (4 + 012) = y (4) + h f(xo, do) = y(4) + hot(4:1) = 1 + 02 (2) 1 + 0.2 2 So y (412) =jot = Asmiri f (219) [from 1)] *(4-4)= y2 = 9, + = 114 0:2 4(1:9, 10) 22 L • (01) ² + 6. 1)] - 1 + 0.2 = 1 + 0.27 0.55 = 1.21 So, y(4.4) = 1-21 Aghion, " (104-1812) = Y = Yg + h fM4, 2) [from 19] = 1.21 + 0-2 f (4.49 1021)

= 1.21 + Or 2 x ding (1-313-46-30) 2 1121 of 0.2 x 0.60775 = 1.21 +0.12 155 F 1.21 + 0.12 Round to two decimal places) 1.33 so y(46) = 1.33 Asun 133 + 0-2 4.8 (4.6 +012) = 4 Yg + h f(23, 43) [from (y) = 133+ 012 f (4.6, 1.33) * ((1333° 4 (133)] 01.33 + 0.1347 ů 1.33 +0.13 Round to two decimal places) - 1.46 So, y (4.8) 21:46 uker's Method 4.2 I 4:4 xn 2 3 4 4.6 4.8 1.33 1.46