what am i doing wrong? http://i52.photobucket.com/albums/g34/b ... 7/math.jpg[/img]
T thebenji New member Joined Sep 2, 2006 Messages 31 Sep 26, 2006 #1 what am i doing wrong? http://i52.photobucket.com/albums/g34/b ... 7/math.jpg[/img]
skeeter Elite Member Joined Dec 15, 2005 Messages 3,215 Sep 26, 2006 #2 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)
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)