Question

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' + y = 0 , y(0) = 4 , y' (0) = 4

(f) y'' + 3y ' = 0, y(0) = −2 , y'(0) = 3

(g) 4y'' − y = 0 , y(−2) = 1 , y'(−2) = −1

Answer 1