I am horrible at matlab so if someone can help me with part (a) then I will do the rest myself.
Solve the following initial value problems numerically, then plot the solutions. Based on your plots, predict what happens to each solution as t increases. In particular, if there is a limiting value for y, either finite or infinite, find it. If it is unclear from the plot you've made, try replotting on a larger interval. Another possibility is that the solution blows up in finite time. If so, estimate the time when the solution blows up. Try to use the qualitative methods of Chapter 6 to confirm your answers.
(a) y'= e^(-3*t) + 1/(1+y^2), y(0)=-1.