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8.1 supplemental HW


1.)  Which of the following could be the general solution to the differential equation whose direction field is given below:

\textbf{A)}  $y = t + C$ \hfill ~~~~~
\textbf{B)} $y =2t + C$ \hfill ~\hfill ~ \hfill ~

\textbf{C)}  $y = \frac{1}{2}t + C$ \hfill ~~~~~
\textbf{D)} $y = -\frac{1}{2}t + C$ \hfill ~\hfill ~ \hfill ~

\textbf{E)}  $y = -t + C$ \hfill ~~~~~
\textbf{F)} $y =-2t + C$ \hfill ~\hfill ~ \hfill ~

\textbf{G)} $y = ln(t) + C$ \hfill 
\textbf{H)} $y =C$ \hfill ~\hfill ~ \hfill ~

\textbf{I)} $y = \frac{Ct^3}{3}$\hfill~~~~~~~~~~~
\textbf{J)} $y = \frac{t^3}{3} + C$ \hfill ~\hfill ~ \hfill ~ 




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2.)  Circle  the differential equation whose direction field is given below:

\textbf{A)}  $y' = t^2$ \hfill ~~~~~
\textbf{B)} $y' =\frac{1}{2}$ \hfill ~\hfill ~ \hfill ~

\textbf{C)} $y' = 1$ \hfill~~~~~
~~\textbf{D)} $y' =-1$ \hfill ~\hfill ~ \hfill ~

\textbf{E)} $y' = y + 1$\hfill~~
~~\textbf{F)} $y' = y - 2$ \hfill ~\hfill ~ \hfill ~

\textbf{G)} $y' =  (y + 1)(y - 2)$ \hfill \hskip 0.8pt
\textbf{H)} $y' = (y + 1)^2(y - 2)^2$ \hfill ~\hfill ~ \hfill ~

\textbf{I)} $y' =  (y + 1)(y - 2)^2$\hfill~~~
\textbf{J)} $y' = (y + 1)^2(y - 2)$ \hfill ~\hfill ~ \hfill ~ 


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4.)  Circle the general solution to the differential equation whose direction field is given below:

\textbf{A)}  $y = t + C$ \hfill ~~~~~
\textbf{B)} $y =t^2 + C$ \hfill ~\hfill ~ \hfill ~

\textbf{C)} $y = e^t + C$ \hfill~~~~~
\textbf{D)} $y = Ce^t + t + 1$ \hfill ~\hfill ~ \hfill ~

\textbf{E)} $y = Ce^t$\hfill~~~~~~~~~~
\textbf{F)} $y = e^t + t + C$ \hfill ~\hfill ~ \hfill ~

\textbf{G)} $y = ln(t) + C$ \hfill 
\textbf{H)} $y =C$ \hfill ~\hfill ~ \hfill ~

\textbf{I)} $y = sin(t) + C$\hfill~~~
\textbf{J)} $y =cos(t) + C$ \hfill ~\hfill ~ \hfill ~ 


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5.)  Which of the following could be the general solution to the differential equation whose direction field is given below:

\textbf{A)}  $y = t + C$ \hfill ~~~~~
\textbf{B)} $y =t^2 + C$ \hfill ~\hfill ~ \hfill ~

\textbf{C)} $y = e^t + C$ \hfill~~~~~~
\textbf{D)} $y = \frac{(t - 1)^3}{3} + C$ \hfill ~\hfill ~ \hfill ~

\textbf{E)} $y = Ce^t$\hfill~~~~~~~~~~
\textbf{F)} $y =  \frac{t^3}{3} + C$ \hfill ~\hfill ~ \hfill ~

\textbf{G)} $y = ln(t) + C$ \hfill 
\textbf{H)} $y =C$ \hfill ~\hfill ~ \hfill ~

\textbf{I)} $y = \frac{Ct^3}{3}$\hfill~~~~~~~~~~~
\textbf{J)} $y = \frac{C(t - 1)^3}{3}$ \hfill ~\hfill ~ \hfill ~ 


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6.)  Circle  the differential equation whose direction field is given below:

\textbf{A)}  $y' = t^2$ \hfill ~~~~~~~~~~~~~
\textbf{B)} $y' =y+3$ \hfill ~\hfill ~ \hfill ~

\textbf{C)} $y' = e^t$ \hfill~~~~~~~~~~~~~
\textbf{D)} $y' =t + 1$ \hfill ~\hfill ~ \hfill ~

\textbf{E)} $y' = t-y$\hfill~~~~~~~~~~~
\textbf{F)} $y' = y-t$ \hfill ~\hfill ~ \hfill ~

\textbf{G)} $y' = (1 + y)(1-y)$ \hfill 
\textbf{H)} $y' =y(1+y)$ \hfill ~\hfill ~ \hfill ~

\textbf{I)} $y' = t(1-t)$\hfill~~~~~~~~~~
\textbf{J)} $y' =y(1-y)$ \hfill ~\hfill ~ \hfill ~ 

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