Solve the initial value problem. Use the method of undetermined
coefficients when finding a particular solution. y'' + y = 8 sin t;
y(0) = 4, y' (0) = 2
Using the appropriate general solution you found in the problem
above, solve the following initial value problems. Sketch a graph
of the solution that captures the initial condition, the limiting
behaviour of the solution as t → ∞ and t → −∞ and the sign of the
solution (positive or negative) in these limits (look at the
dominant terms).
(c) 2y'' - 3y' + y = 0 , y(2) = 1 , y'(2) = 1
(e) 6y'' − 5y' +...