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Use Green's function method to solve the differential equation: dy(x) –4y(x)= f(x) dx? subject to y'(0)= y(t)=0. Find y(x) if f(x)=x.

Use Green's function method to solve the differential equation: dy(x) –4y(x)= f(x) dx? subject to y'(0)= y(t)=0. Find y(x) if f(x)=x.

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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Use Green's function method to solve the differential equation: d²y(x) – 4 y(x)= f(x) dx? subject to y'(0)= y(t)=0. Find y(x) if f(x)=x. Write the general solution of the differential equation in terms of the Green's function: d²y(x) --k’y(x)= f(x), O<x<L dx? y(0) = y(L)=0 Now, solve the same equation in the range -<x<o∞ with y(to)<∞.
Transcribed Image Text:Use Green's function method to solve the differential equation: d²y(x) – 4 y(x)= f(x) dx? subject to y'(0)= y(t)=0. Find y(x) if f(x)=x. Write the general solution of the differential equation in terms of the Green's function: d²y(x) --k’y(x)= f(x), O<x<L dx? y(0) = y(L)=0 Now, solve the same equation in the range -<x<o∞ with y(to)<∞.
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