Use each ofthe Adams-Bashforth methods to approximate the solutions to the following initial-value problems. In each case, use starting values obtained from the Runge-Kutta method of order four. Compare the results to the actual values. ~ t a. y' = y/t (y/t) , 1 < t < 2, y(l) = I, with A = 0.1; actual solution y(r) = . 1 + In t b. y' = l+y/r-Ky/r)2 , 1 < / < 3, y(l) = 0, with/; = 0.2; actualsoluliony(r) = rtan(ln?). c. y' -- (y + l)(y + 3), 0 < t < 2, y(0) - -2, with h 0.1; actual solution y(r) -3 + 2/(1 -be-2 '). d. y' = 5y + 5?2 + 2r, 0 < r < 1, y(0) = 1/3, with h 0.1; actual solution y(t) t 2 + l 5e-

Math121 Chaapptterr77NNoottess Lesson7.4–PropertiesandApplicationsofLogarithms Thesetipsshouldhelpyougetthroughthishw.J • log (1)=0 x • log (x)=1 • log (a )=rlog (xa x • log (a )=x • a loga(x)=x • log(x)+log(y)=log(xy) • log(x/y)=log(x)–log(y) EXAMPLE1. Usethepropertiesoflogarithmstocondensethefollowing expressionasmuchaspossible,writingtheanswerasasingle termwithacoefficientof1.Allexponentsshouldbepositive. log(y)+log(19) (Usingourtipsatthetopofthepage,we canseethataddingtwologarithmsresu