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Quiz 1 Form {\bf A}\hfil \break
Sept 1, 2017

1.) Determine the \underbar{order} of the given differential equations and also state whether the equation is  \underbar{linear or nonlinear}:


[3]~ 1a.)  $t + yy' = 1$ is a 
$\underline{\hskip 0.6in}$ order $\underline{\hskip 1.5in}$ differential equation.


[3]~ 1b.)  $ty + y' = 1$ is a 
$\underline{\hskip 0.6in}$ order $\underline{\hskip 1.5in}$ differential equation.
\vskip 20pt

[14]~ 2.)  Solve and state where the solution is defined:  $t^4y' + 4t^3y = {1 \over t}$

\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill\vfill
%$t^4y' + 4t^3y = {1 \over t}$

%$(t^4y)' = {1 \over t}$

%y = t^{-4}[ln|t| + c]


Solution:  $\underline{\hskip 2in}$ 
\hfill
Domain:  $\underline{\hskip 1.3in}$ 



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[10]~ 2.)  Solve $sin(t) y' + y cos(t) = 5$ 
 \hfil \break(hint:  this is a short problem if you are observant).

$sin(t) y' + y cos(t) = 5$

 $(sin(t) y)'  = 5$  
 
  $\int (sin(t) y)' dt  = \int 5 dt$  

 $\sin(t) y = 5t + C$  

 $ y  = {5t + C \over sin(t)}$  




Answer:$\underline{~~ y  = {5t + C \over sin(t)}~~}$
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