Question

Answer 1

Problem 5 Answer:

y prime = 3 + 2y dy/dt = 3 + 2y rightwardsdoublearrow integrating both sides integral dy/3 + 2y = integral dt ln (3 + 2y)/2 = t + c ln (3 + 2y) = 2t + c prime 3 + 2y = c_1 e^2t 2y = c_1 e^2t - 3 direction field y(t) = c_1 e^2t/2 -3/2 \r\n as y prime = 3 + 2y y(t) = c_1 e^2t/2 - 3/2 t > infinity = at y(0) > -1.5 lim_t rightarrow infinity y(t) rightarrow + infinity. When at y(0) < 1.5 lim_t rightarrow infinity y(t) rightarrow -infinity