Step 1

-2y = 0 when y = 0. Thus the constant y(t) = 0 is a particular solution.

Step 2

Separate the variables and integrate both sides,

where C = e^B if y > 0, and C = -e^B if y < 0.

Step 3

General solution: y(t) = Ce-^2t, where C is any constant (C can be 0 from Step 1).

Step 4

Substitute 1 for t and - 5 for y, and solve for C. -5 = Ce^-2·1, -5 = Ce^-2, C = -5e². Particular solution: y(t)= -5e²e^-2t = -5e^(2-2t). The graph of the solution is shown in Figure 14.1.4.