The particular solution of y" + 10y' + 25y = e−5t is yp(t) = 1⁄2t²e-5t Find the null solution yn (t) of the ODE. Show that the linear combination yn (t) + y(t) is also a solution to the ODE. For initial conditions y(0) = 1 and y'(0) = 0, find the complete solution.
The particular solution of y" + 10y' + 25y = e−5t is yp(t) = 1⁄2t²e-5t Find the null solution yn (t) of the ODE. Show that the linear combination yn (t) + y(t) is also a solution to the ODE. For initial conditions y(0) = 1 and y'(0) = 0, find the complete solution.
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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The particular solution of y''+10y'+25y=e^(-5t) is Y_p(t)= (1/2)t^2e^-5t. Find the null solution ?_n(?) of the ODE. Show that the linear combination ?_n(?) + ?_p(?) is also a solution to the ODE. For initial conditions ? (0) = 1 and ?'(0) = 0, find the complete solution.
Transcribed Image Text:The particular solution of y" + 10y' + 25y = e−5t is yp(t) = 1⁄2t²e-5t
Find the null solution yn (t) of the ODE.
Show that the linear combination yn (t) + y(t) is also a solution to the ODE.
For initial conditions y(0) = 1 and y'(0) = 0, find the complete solution.
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