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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 March 11th, 2011, 10:00 AM #1 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Linear differential equations Problem: Use the integrating factor method to solve the following linear differential equation x dy/dx - y = x I used the same method as I did last night with the other equations and found the integrating factor to be ?(x)=e^?-1/x dx = e^-ln(x) = -x (or in this case would it be just (x) ? ) Then Multiplying the standard form equation by (-x) , -x(dy/dx)-y= -x Integrating to get y=1/2 x + A / x Im a bit unsure on it March 11th, 2011, 10:12 AM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Linear differential equations Now try it.  March 11th, 2011, 10:26 AM #3 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Re: Linear differential equations y= - (ln(x) +A / x) March 11th, 2011, 10:36 AM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Linear differential equations We have in standard form: Multiplying through by gives: Integrate w.r.t. x: March 11th, 2011, 11:38 AM #5 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Re: Linear differential equations oh yes, i made the mistake on multiplying by the integrating factor. my next equation cos(t) dx/dt + x sin(t) = cos^2 (t) Re write in Std.form, divide by cos(t) dx/dt + x (sin(t)/cos(t)) = cos(t) Obtain Integrating factor, ?(x)=e^?sin(t)/cos(t) = e^-ln(cos(t)) = -cos(t) or is it 1/cos(t) March 11th, 2011, 12:37 PM #6 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Linear differential equations It is , since by the properties of logarithms, we have . This transforms your equation in standard form to: Then you have: March 11th, 2011, 01:09 PM #7 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Re: Linear differential equations oh ok, yes i thought the laws of logs would be involved. so then i integrate d/dx (x sect)=1 ? March 11th, 2011, 01:19 PM #8 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Linear differential equations You integrate: w.r.t. t (Notice the slight difference in what I wrote and what you wrote. ) March 11th, 2011, 01:32 PM #9 Senior Member   Joined: Feb 2011 Posts: 150 Thanks: 0 Re: Linear differential equations oh yes it was suposed to say t. x sec(t) = x + C , do i divide by sec(t)  March 11th, 2011, 02:21 PM #10 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Linear differential equations Or multiply through by cos(t), same thing. Although your right side should be t + C (recall we integrated with respect to t). Tags differential, equations, linear 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 byrnesj1 Differential Equations 1 July 26th, 2012 10:48 AM bobby Differential Equations 3 October 22nd, 2011 05:48 AM Sefrez Differential Equations 1 October 10th, 2011 07:10 AM Steel Differential Equations 6 December 5th, 2010 11:39 AM jokes_finder Differential Equations 3 November 20th, 2010 09:52 AM

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