Question

please answer b. and c.

Problem 1. Consider the differential equation given by (a) On the axes provided below, sketch a slope field for the given differential equation at the nine points indicated. locales de mor t e wold qolution to the given differential equation with the initial condition

Answer 1

ses" : Guien chifferential iguation is ty ~ fla,y) du 2 - 4 oil (6) y = f(x) is the particuler solution with y(o)= 166): 3 dil. Yo = 3, No 2 o initially starting at tro de nozo with step size ile he oil, we have to find & (0.2) d.l. we will find y at 0.2=x using Euler's method Yn a Yn ith f(an-i, Yn-i) a Now, y, a Yo + oil fldo, you = 3+ Oil F 0,3) 3+0:1 (073) using lo = 370 = 3 y Now, Yzz y + oolf (x1, 4, ) - here = Ho + LX h = 0 + IXO) 2 = 011 Y = 3 + oil f (011, 3) i using V = 3+01 (8.193 ) = 3 + 0.01x1.5 = 3 +0.015 = 3.015 1 y2 csannfalonik) = y2 = 3:015 CamScanner

(c) Bylves & dy = 7 de 2 Integrating both sides u dx + enc ic is an integration constant 2 + enco eny = eny-ene = en (4) - The cex'/] (3) flo) = 3 = y0) = 3 initially By (3): 32 ceo I (23 a By (3): S4 2 3 2314 Now, o we have to find f10.2) 2 y 10.2) = floor) 3€ = 320.01 f(0, 2) = 3.030 Isos Cs Scanned liflo. 2) 3.03 01 CamScanner