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October 10th, 2012, 12:46 PM  #1 
Newbie Joined: Oct 2012 Posts: 18 Thanks: 0  (Q) Linear combinations of solutions
Hi! First post here, looking forward to browsing this forum I've got a question. I just started studying Fourier analysis, and I've come upon a question that I couldn't figure out. Q: Suppose u1 and u2 are both solutions of the linear differential equation L(u) = f, where f != 0. Under what conditions is the linear combination c1u1 + c2u2 also a solution of this equation? A: c1 +c2 = 1. Could someone explain why this is? 
October 10th, 2012, 01:10 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,852 Thanks: 742  Re: (Q) Linear combinations of solutions
L(c1u1 + c2u2) = c1L(u1) + c2L(u2) = c1f + c2f = (c1 + c2)f. Clear enough? 
October 10th, 2012, 02:24 PM  #3 
Newbie Joined: Oct 2012 Posts: 18 Thanks: 0  Re: (Q) Linear combinations of solutions
Actually, yes! I love pure algebraic explanations when they're simple enough. Cheers! 

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combinations, linear, solutions 
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