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 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
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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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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

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