[MOVED] Differential Eqn- du/dt = e^(3u+3t)

thebenji

New member
Joined
Sep 2, 2006
Messages
31
what am i doing wrong?

math.jpg


http://i52.photobucket.com/albums/g34/b ... 7/math.jpg[/img]
 
du/dt = e<sup>3u + 3t</sup>

du/dt = e<sup>3u</sup>*e<sup>3t</sup>

separate variables ...

e<sup>-3u</sup> du = e<sup>3t</sup> dt

integrate ...

(-1/3)e<sup>-3u</sup> = (1/3)e<sup>3t</sup> + C

multiply both sides by -3 ...

e<sup>-3u</sup> = -e<sup>3t</sup> + C

log both sides ...

-3u = ln(-e<sup>3t</sup> + C)

u = (-1/3)ln(-e<sup>3t</sup> + C)

initial condition u(0) = 15 ...

15 = (-1/3)ln(-1 + C)

-45 = ln(-1 + C) ... C = e<sup>-45</sup> + 1

u = (-1/3)ln(-e<sup>3t</sup> + e<sup>-45</sup> + 1)
 
Top