Chapter 1.6, Problem 37E

Eight differential equations and four phase lines are given below. Determine the equation that corresponds to each phase line and state briefly how you know your choice is correct.

(i) $\frac{dy}{dt}=y\cos \left(\frac{\text{π}}{2},y\right)$ (ii) $\frac{dy}{dt}=y-y^2$ (iii) $\frac{dy}{dt}=\left|y\right|\sin \left(\frac{\text{π}}{2},y\right)$ (iv) $\frac{dy}{dt}=y^3-y^2$

(v) $\frac{dy}{dt}=\cos \left(\frac{\text{π}}{2},y\right)$ (vi) $\frac{dy}{dt}=y^2+y$ (vii) $\frac{dy}{dt}=y\sin \left(\frac{\text{π}}{2},y\right)$ (viii) $\frac{dy}{dt}=y^2-y^3$