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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:


\rightline{\textbf{A)}  $y = t + C$, ~~~~~~$y' =1$ }

\rightline{\includegraphics[width = 2.2in, height = 2.2in]{SF1}}  %% export as pdf file 

\hrule
\vskip 0.3in
\leftline{\textbf{E)}  $y = -t + C$ }
\leftline{\includegraphics[width = 2.2in, height = 2.2in]{SFminus1}}  %% export as pdf file 

\vskip -2.5in
\centerline{\textbf{B)} $y =2t + C$}
\centerline{\includegraphics[width = 2.2in, height = 2.2in]{SF2}}  %% export as pdf file 

\vskip -2.5in
\rightline{\textbf{C)}  $y = \frac{1}{2}t + C$, ~~~~~~~~~~$y' =\frac{1}{2}$ }
\rightline{\includegraphics[width = 2.2in, height = 2.2in]{SFhalf}}  %% export as pdf file 

\hrule
\vskip 10pt

\leftline{\textbf{I)} $y = \frac{Ct^3}{3}$}
\leftline{\includegraphics[width = 2.2in, height = 2.2in]{SFcTcubed}}  %% export as pdf file 

\vskip -2.5in
\centerline{\textbf{J)} $y = \frac{t^3}{3} + C$}
\centerline{\includegraphics[width = 2.2in, height = 2.2in]{SFtsquared2}}  %% export as pdf file 

\vskip -2.5in
\rightline{\textbf{K)} $x^2 + y^2 = C $}
\rightline{\includegraphics[width = 2.2in, height = 2.2in]{SFcircle}}  %% export as pdf file 

\eject

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

\rightline{\textbf{F)} $y' = y - 2$}
\rightline{~~~~~~~~\includegraphics[width = 2.2in, height = 2.2in]{SFyminus2}}  
%% export as pdf file 

\hrule

\vskip 0.3in
\leftline{\textbf{G)} $y' =  (y + 1)(y - 2)$}
\leftline{\includegraphics[width = 2.2in, height = 2.2in]{SFy2}}  %% export as pdf file 

\vskip -2.5in
\centerline{\textbf{I)} $y' =  (y + 1)(y - 2)^2$}
\centerline{\includegraphics[width = 2.2in, height = 2.2in]{SFy2squared}}  %% export as pdf file 

\vskip -2.5in
\rightline{\textbf{H)} $y' = (y + 1)^2(y - 2)^2$}
\rightline{\includegraphics[width = 2.2in, height = 2.2in]{SFy2pos}}  %% export as pdf file 

\hrule
\vskip 20pt
\centerline{\textbf{A)}  $y' = t^2$}
\centerline{\includegraphics[width = 2.2in, height = 2.2in]{SFtsquared2}}  %% export as pdf file 

\vskip -2.5in
\leftline{\textbf{K)} $y = -\frac{t}{y}$}
\leftline{\includegraphics[width = 2.2in, height = 2.2in]{SFcircle}}  %% export as pdf file 


\vskip -2.5in
\rightline{\textbf{J)} $y' = (y + 1)^2(y - 2)$}
\rightline{\includegraphics[width = 2.2in, height = 2.2in]{SFy21squared}}  %% export as pdf file 



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