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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 May 13th, 2013, 05:27 AM #1 Member   Joined: Apr 2013 Posts: 42 Thanks: 1 differential equation Given is the differential equation where b is constant and real. How do I show that for any the solution to the equation is equal to , where and A and B are constant and real? And I also wonder how to determine for b=2, y(0)=2 and y'(0)=8 the solution to the differential equation? May 13th, 2013, 05:36 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: differential equation I would multiply the ODE by , then write the characteristic equation and use the quadratic formula to determine the roots. What do you find? May 13th, 2013, 06:44 AM #3 Member   Joined: Apr 2013 Posts: 42 Thanks: 1 Re: differential equation I find . So ? Almost there, only I have a instead of in the sinus and cosinus... May 13th, 2013, 07:26 AM #4 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: differential equation That is a second order, linear homogeneous differential equation. The theory says that the set of all solutions is a vector space of dimension 2 which means that every solution can be written as a linear combination of two functions that satisfy the equation. Clearly is a linear combination of and . So it is sufficient to show that and satisfy the differential equation and are independent. May 13th, 2013, 08:47 AM #5 Member   Joined: Apr 2013 Posts: 42 Thanks: 1 Re: differential equation I forgot to take the square root of . When I do that, the answer is correct. And the second question is just substituting b by 2 and equate y and y' to the given values? It gives me A=2 and B=5/4 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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