d²y dx² -y=xe*
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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Question
Differential Equations
Please, show all the work and every step
Transcribed Image Text:(9) --y=xe*
d²y
dx²
HINT: For homogenous solution, substitute y = Aex to find roots of
characteristic equations_r₁= 1 and r2=-1; For particular solution use undetermined
coefficients of the form yp-axex. This does not work for original ODE, so try
yp-ax2ex + bxex which gives a=1/4 and b=-1/4;
ANSWER: y = Ae-x+ Bex+x2ex /4 - xex/4
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