To get a feel for higher order ODEs, show that the given functions are solutions and form a basis on any interval. Use Wronskians. In Prob. 6, x > 0, cos x, sin x, x cos x, x sin x, y iv + 2y + y = 0
Chapter 3, P R O B L E M S E T 3 . 1 #3
To get a feel for higher order ODEs, show that the given functions are solutions and form a basis on any interval. Use Wronskians. In Prob. 6, x > 0,
cos x, sin x, x cos x, x sin x, yiv + 2y" + y = 0
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Answer
The Wronskian of sin x and cos x is 1. By the essential supremum criterion, we have: 2x si…View the full answer
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