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\noindent {\bf Problem statement} Find the general solution of the differential
equation $$e^{-y}{\displaystyle{{dy}\over{dt}}}+2\cos t=0\,.$$


 
\noindent a) Sketch the solutions corresponding to several values of
the constant of integration, $C$. Does every value of the constant of
integration correspond to a solution curve? If not, which $C$'s do
occur?

\medskip

\noindent b) Do all the solutions have the same domain? Explain.

\medskip

\noindent c) Sketch the direction field associated with this equation
and superimpose your sketches of solution curves on the direction
field. (Suggestion for sketching the direction field: sketch at
several points along the line $t=0$, then at the corresponding points
along the lines $t=\pi/6$, $\pi/3$, $\pi/2$, etc.)

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