y +2y + y = 0, you = y (o = 0 6. Verify that y₁ (t) = t is a solution of t²y" -t(t+2)y' + (t+2)y = 0 for t > 0. Use the method of reduction of order to find a second solution y2(t) of the differential equation so that {y1(t), y2(t)} is a fundamental set of solutions. 7. Use the method of undetermined coefficients to find the general solution of the linear es

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

5. Please show all equations 

y +2y + y = 0,
you
=
y (o = 0
6. Verify that y₁ (t) = t is a solution of t²y" -t(t+2)y' + (t+2)y = 0 for t > 0. Use the method of
reduction of order to find a second solution y2(t) of the differential equation so that {y1(t), y2(t)} is
a fundamental set of solutions.
7. Use the method of undetermined coefficients to find the general solution of the linear es
Transcribed Image Text:y +2y + y = 0, you = y (o = 0 6. Verify that y₁ (t) = t is a solution of t²y" -t(t+2)y' + (t+2)y = 0 for t > 0. Use the method of reduction of order to find a second solution y2(t) of the differential equation so that {y1(t), y2(t)} is a fundamental set of solutions. 7. Use the method of undetermined coefficients to find the general solution of the linear es
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