20. ty+ (+1)y-1. y(ln 2) 1. 10 In each of Problems 21 through 23: (a) Draw a direction field for the given differential equation. How do solutions appear to behave as I becomes large? Does the behavior depend on the choice of the initial value a Let do be the value of a for which the transition from one type of behavior to another occurs Estimate the value of ao. (b) Solve the initial value problem and find the critical value do exactly. (c) Describe the behavior of the solution corresponding to the initial value ao. 221. y-ly 2 cost, = 22. 2y-ye 223. 3y-2ye y(0)=a y(0)=a y(0) = a In each of Problems 24 through 26: (a) Draw a direction field for the given differential equation. How do solutions appear to behave as t→0? Does the behavior depend on the choice of the initial value a? Let do be the value of a for which the transition from one type of behavior to another occurs. Estimate the value of ag. (b) Solve the initial value problem and find the critical value ao exactly. (c) Describe the behavior of the solution corresponding to the initial value ao. 24. ty+ (+1)y = 2te", y(1)=a, t>0 225. ty + 2y (sint)/t. у(-л/2)=a, 1<0 226. (sint)y' + (cost)y = e', y(1)=a, 0<t< 227. Consider the initial value problem y+y=2 cost, y(0)=-1. Find the coordinates of the first local maximum point of the solution for 1 > 0. 228. Consider the initial value problem