My Math Forum Differential equation

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 April 12th, 2007, 10:20 PM #1 Newbie   Joined: Apr 2007 Posts: 6 Thanks: 0 Differential equation somebody that can help me solve this? find the general solution dy/dt=-2y I know that the preposition dy/dt=ay gives y=ce^at and the answer is supposed to be y=ac^-2t, but proving this was worse...
 April 13th, 2007, 05:09 AM #2 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 In other words, you are saying that: y' + 2y = 0 If we had initial values, we could solve this by Laplace transformations, but since we don't, we'll have to go by a different route. We'll have to say that r^2 + 2 = 0 and then solve for the complex number r, and then use the two real parts of e^r as the terms that will give us the solution to the problem.
 April 14th, 2007, 01:43 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2202 Multiply by e^(2t), then integrate.
 May 6th, 2007, 03:29 PM #4 Senior Member   Joined: May 2007 Posts: 402 Thanks: 0 dy/dt = -2y multiply with dy and divide with y and you get: dy/y=-2dt integrate and: ln(y)-ln(y0)=-2t ln(y)=-2*t+ln(y0) y=exp(-2t+ln(y0)) y=y0*exp(-2t) where y0 is the initial value!
May 6th, 2007, 11:36 PM   #5
Global Moderator

Joined: Dec 2006

Posts: 20,919
Thanks: 2202

Quote:
 Originally Posted by Infinity If we had initial values, we could solve this by Laplace transformations, . . .
One can write y0 for y(0) and use the Laplace transform method. Don't expect to get y=ac^-2t, since the correct solution is y = y0e^(-2t).

Alternatively, one can solve the characteristic equation, r + 2 = 0 (not r^2 + 2 = 0), and hence write down the answer.

 Tags differential, equation

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post PhizKid Differential Equations 0 February 24th, 2013 10:30 AM cheyb93 Differential Equations 3 February 7th, 2013 09:28 PM mathkid Differential Equations 0 October 9th, 2012 08:01 AM tomislav91 Differential Equations 1 May 30th, 2012 07:28 AM tsl182forever8 Differential Equations 2 March 14th, 2012 03:12 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top