Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please do number 2
**Exercises** 1. Find the general solution of \( x'' + tx' + x = 0 \) given that \( x = e^{-t^2/2} \) is one solution. 2. Show that \( x_1(t) = t \) is a solution of the equation \( x'' - tx' + x = 0 \). Use reduction of order to find a second solution \( x_2(t) \).
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Transcribed Image Text:**Exercises** 1. Find the general solution of \( x'' + tx' + x = 0 \) given that \( x = e^{-t^2/2} \) is one solution. 2. Show that \( x_1(t) = t \) is a solution of the equation \( x'' - tx' + x = 0 \). Use reduction of order to find a second solution \( x_2(t) \).
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