Question

pi DIFFERENTIAL EQUATIONS CHAPTER 2 FIRST-ORDER DIFFERE dx - x = 2y2 y(t) = 5 RE Ri = E, i(0) = in. L. R. E, i, constants a = k(T – T.). TO) = To, k, Tm, T, constants 31. x + y = 4x + 1, y(1) = 8 32. y' + 4xy = rer? y(0) = -1 dy + y = ln x, y(1) = 10 dx 34. x(x + 1) + xy = 1, yle) = 1 35. y' – (sin x)y = 2 sin x, y(7/2) = 1 56. y' + (tan x)y = cos²x, y(0) = -1 In Problems 37-40 proceed as in Example 6 to solve the given initial-value problem. Use a graphing utility to graph the continuous function y(x). 37 dy (0) = 0, where f(x) = To, <x<3 x>3 38. + y = f(x), y(0) = 1, where

28, 30, 36.

Answer 1

yox - 2 =942,90= 5 so we can write D.E. as de = ly 1 This liner in randy so I.F. so soln is x. If = SI. FX 29 dy & C - & /y = Sxrydy +C y = 24 + 6 x= 242 +cy use (1)=5 = 50+ 56 = = = so solnis x=242 - 49

3 = (T-Tm), TO) = T, K, Tm, 8 to Gensteet sv on variable serable ( dt = klat IT-Tm - In 17-Tm) = kt+C. giren T(o) = To In To-Tml = kote =) (= In/To-Tm) so In/T-Tml = x++ In/To-Tm) InIT_Tm/-In) To-Tm/= kt 76m To-Tm kt T- Tm= (To-Tm) e T(t) = TM t (To-Tm) e etx

(36) y'+ (tanxly = cos & 9 (0) = -1 Sol we can write a ar t This tanny = cos lineras y anda so So I.F Stanndy e - = = Inseca = e seen so son is Y. IF = S I. FX Code + c y.secn= (seexxcondate = Sconda te qe secx = sinnte = sinn cosnt Close use y.(o)= -1 I= .. - 9 = Sinh Cap – CP | _ 0 SA