Cinita Brown,
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Several Burdens are mentioned in my book: Carroll (W.C.), John, Joseph, and William. ..On Ancestry.com, I could not find the death date of this William but did see that he was born in 1841 in Missouri.
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Quoting the "Wm. Burden" entry in http://www.11texascav.org/content/company-b-2

"William Burden Mustered into the Texas Militia on May 25, 1861 at Gainesville. He was 22 years old at the time. ..Private Burden was wounded severely in hip during the battle of Murfreesboro on December 31, 1862. He was taken prisoner by federals. No further record."
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Fold 3 records: printed "Confederate prisoner in Hospital No. 1 in Murphreesboro TX, April 3, 1863." .. handwritten "in hospital."
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You stated that George Wash Burden had siblings: Joseph, William, and Nancy, so I trust that you know if William died in the hospital in 1863.
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I look forward to your response.
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Patti, prochette@Juno.com