ORDINARY DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS Solve each of the following by using Laplace transforms and check solutions. Ans. Y t 44. Y"+tY' Y = 0, Y(0) = 0, Y'(0) = 1. 45. tY"+(1-2t) Y'2Y = 0, Y(0) = 1, Y'(0) = 2. 46. tY"(t-1)Y'Y = 0, Y(0) = 5, Y() = 0. 47. Find the bounded solution of the equation - which is such that Y(1) = 2. Ans. Y et Ans. Y 5e-t 12y" +tY' + (t-1) Y = 0 Ans. 2J (t)/J (1)