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EXERCISES 1. Find the general solution of x" + tx' + x = 0 given that x = e-t²/2 is one solution. 2. Show that xi(t) = t is a solution of the equation r" - tx' + x = 0. Use reduction of order to find a second solution x2(t).

EXERCISES 1. Find the general solution of x" + tx' + x = 0 given that x = e-t²/2 is one solution. 2. Show that xi(t) = t is a solution of the equation r" - tx' + x = 0. Use reduction of order to find a second solution x2(t).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**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 \( x_2(t) \).
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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