Chapter D1.4, Problem 31E

Explain why or why not Determine whether the following statements are true and give an explanations or counterexample

a.    The general solution of $y^{\prime }\left(t\right)=2y-18$ is $y\left(t\right)=2e^{2t}+9$.

b.    If k > 0 and b > 0, then $y\left(t\right)=0$ is never a solution of $y^{\prime }\left(t\right)=ky-b$

c.    The equation $y^{\prime }\left(t\right)=ty\left(t\right)+3$ is separable and can be solved using the methods of this section.

d.    According to Newton’s Law of Cooling, the temperature of a hot object will reach the ambient temperature after a finite amount of time