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October 21st, 2009, 06:57 PM   #1
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Differential Equations

Hi, I have been working on this differential equation problem that is in the attachment i was wondering if someone could give me any advice to if this is the correct way of doing this and if i have the correct answer.

sorry about the poor quality in scanning

Matt
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 November 13th, 2009, 01:34 AM #2 Member   Joined: Nov 2009 Posts: 72 Thanks: 0 Re: Differential Equations I'm having a bit of a problem reading your handwriting, but it looks as though to find a particular solution of the ODE, you set $y(x)=S+Rx+P\sin{x}+Q\cos{x}$, and then found P = 3/13, Q = 2/13, S = 7/8, and R = 3/4, which is right. But then for some reason in your final answer you switched it around to $y(x)=P\sin{x}+Q\cos{X}+Ae^{-Sx}+Be^{-Rx}$, which doesn't seem right. How I would do it: the particular solution of the ode, as you found, is $y_p(x)=\frac{7}{8}+\frac{3}{4}x+\frac{3\sin{x}+2\c os{x}}{13}$, and the general solution to the homogeneous problem is $y(x)=C_1e^x\sin{\ x\sqrt{3}}+C_2e^x\cos{\ x\sqrt{3}}$, and so the general solution to the inhomogeneous problem is $y(x)=C_1e^x\sin{\ x\sqrt{3}}+C_2e^x\cos{\ x\sqrt{3}}+\frac{7}{8}+\frac{3}{4}x+\frac{3\sin{x} +2\cos{x}}{13}$

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