Find A, B, C, and D

  

2. Consider the differential equation ty + 2y = et. With initial condition y(1) = 1, this has the solution et (t-1) + 1 t y(t) = 85 (B.1) 86 Problem Set B. First Order Equations (a) Verify this using MATLAB, both by direct differentiation and by using dsolve. (b) Graph y(t) on the interval 0 < t < 2. Describe the behavior of the solution near t= 0 and for large values of t. (c) Plot the solutions y, (t) of (B.1) corresponding to the initial conditions y (1) = j, j= -3, -2,...,2,3, all on the same graph, for 0 < t < 4. Use axis to adjust the picture. (d) What do the solutions have in common near t = 0? for large values of t? Is there a solution to the differential equation that has no singularity at t = 0? If so, what is it? wider the initial value problem