Question

Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation 2 drawn, discuss it. If a conclusion cannot be drawn, explain why 4tz' + 2z = cost, given that Z(0) = 2 and 2'(0) - 8. If a conclusion can be Select the correct choice below and fill in any answer boxes to complete your choice. OA. A solution is guaranteed only at the point to = because the functions p(t) = 9(t)= and g(t)= are simultaneously defined at that point. OB. No conclusion can be drawn because the functions p(t) = qt) , and g(t)= are not simultaneously continuous on any interval that contains the point to O C. A solution is guaranteed on the interval << because it contains the point to - and the functions p(t) = 4(t)= and g(t)= are simultaneously continuous on the interval O D. No conclusion can be drawn because the conditions (0) = 2 and z'(0) = 8 do not provide enough information to determine all constants of integration

Answer 1

Differential equation +27+4+2+27= Cest 2(0)=2 and 2(0)=8 A Solution is guaranteed on the interval Bct2o. because et contains the point too and the function P(t)=+2, 914)= 4+, 9CH) = 2 ore Smultaneously continuare on the interval Hence correct option 18 ©)proved