# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{displaymath}v''(t)=-v'(t)(2fracf'(t)f(t)+p(t)){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=358 HEIGHT=41 ALIGN=BOTTOM ALT="displaymath111" SRC="img17.gif"  > '; 
$key = q/{displaymath}y'_2=v'f+vf'hspace.2iny''_2=v''f+2v'f'+vf''.{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=405 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath103" SRC="img13.gif"  > '; 
$key = q/{displaymath}y_2=Ate^-3t+Be^-3t{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=327 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath93" SRC="img8.gif"  > '; 
$key = q/{displaymath}y''_2=v''e^-3t-6v'e^-3t+9ve^-3t{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=366 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath85" SRC="img4.gif"  > '; 
$key = q/{displaymath}y''-ty'+y=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=310 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath119" SRC="img21.gif"  > '; 
$key = q/{displaymath}v=intfracu(t)[f(t)]^2dthspace.2in(***){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=343 HEIGHT=41 ALIGN=BOTTOM ALT="displaymath113" SRC="img18.gif"  > '; 
$key = q/{displaymath}y_2(t)=tintfrace^t^22t^2dt{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=320 HEIGHT=43 ALIGN=BOTTOM ALT="displaymath125" SRC="img24.gif"  > '; 
$key = q/{displaymath}v''f+2v'f'+pv'f=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=335 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath109" SRC="img16.gif"  > '; 
$key = q/{displaymath}y_2(t)=v(t)e^-3t{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=309 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath81" SRC="img2.gif"  > '; 
$key = q/{displaymath}y_2=f(t)intfracu(t)[f(t)]^2dt{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=328 HEIGHT=41 ALIGN=BOTTOM ALT="displaymath117" SRC="img20.gif"  > '; 
$key = q/{displaymath}(v''e^-3t-6e^-3tv'+9e^-3tv)+6(v'e^-3t-3e^-3tv)+6e^-3tv=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=483 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath87" SRC="img5.gif"  > '; 
$key = q/{displaymath}u(t)=e^-intp(t)dthspace.2in(****){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=350 HEIGHT=24 ALIGN=BOTTOM ALT="displaymath115" SRC="img19.gif"  > '; 
$key = q/{displaymath}f''(t)+p(t)f'(t)+q(t)f(t)=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=366 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath99" SRC="img11.gif"  > '; 
$key = q/{displaymath}y_2(t)=v(t)e^-3t=(At+B)e^-3t{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=370 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath91" SRC="img7.gif"  > '; 
$key = q/{displaymath}y''(t)+6y'(t)+9y(t)=0hspace.2in(*){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=367 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath79" SRC="img1.gif"  > '; 
$key = q/{displaymath}v''e^-3t=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=289 HEIGHT=18 ALIGN=BOTTOM ALT="displaymath89" SRC="img6.gif"  > '; 
$key = q/{displaymath}v''f+2v'f'+vf''+p(v'f+vf')+qvf=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=414 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath105" SRC="img14.gif"  > '; 
$key = q/{displaymath}u(t)=e^-int(-t)dt=e^inttdt=e^t^22{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=370 HEIGHT=24 ALIGN=BOTTOM ALT="displaymath121" SRC="img22.gif"  > '; 
$key = q/{displaymath}y(t)=C_1y_1(t)+C_2y_2(t){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=342 HEIGHT=17 ALIGN=BOTTOM ALT="displaymath127" SRC="img25.gif"  > '; 
$key = q/{displaymath}v(f''+pf'+qf)+v''f+2v'f'+pv'f=0{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=409 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath107" SRC="img15.gif"  > '; 
$key = q/{displaymath}y_2=v(t)f(t){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=298 HEIGHT=17 ALIGN=BOTTOM ALT="displaymath101" SRC="img12.gif"  > '; 
$key = q/{displaymath}y''(t)+p(t)y'(t)+q(t)y(t)=0hspace.2in(**){displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=392 HEIGHT=19 ALIGN=BOTTOM ALT="displaymath97" SRC="img10.gif"  > '; 
$key = q/{displaymath}y'_2=v'e^-3t-3e^-3tv{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=326 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath83" SRC="img3.gif"  > '; 
$key = q/{displaymath}y(t)=C_1e^-3t+C_2te^-3t{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=340 HEIGHT=21 ALIGN=BOTTOM ALT="displaymath95" SRC="img9.gif"  > '; 
$key = q/{displaymath}v=intfrace^t^22t^2dt{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=302 HEIGHT=43 ALIGN=BOTTOM ALT="displaymath123" SRC="img23.gif"  > '; 

1;

