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You solve a second order linear differential equation with constant coefficients and find its complimentary function y(x) = Ae²+ Be-2 and its particular solution y₂(x) = -x- Apply the conditions y(0) = 0 and / (0) = 1 to determine the values of A and B. What is the general solution?

You solve a second order linear differential equation with constant coefficients and find its complimentary function y(x) = Ae²+ Be-2 and its particular solution y₂(x) = -x- Apply the conditions y(0) = 0 and / (0) = 1 to determine the values of A and B. What is the general solution?

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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You solve a second order linear differential equation with constant coefficients and find its complementary function \( y_0(x) = Ae^x + Be^{-2x} \) and its particular solution \( y_p(x) = -x - \frac{1}{2} \). Apply the conditions \( y(0) = 0 \) and \( y'(0) = 1 \) to determine the values of \( A \) and \( B \). What is the general solution?
Transcribed Image Text:You solve a second order linear differential equation with constant coefficients and find its complementary function \( y_0(x) = Ae^x + Be^{-2x} \) and its particular solution \( y_p(x) = -x - \frac{1}{2} \). Apply the conditions \( y(0) = 0 \) and \( y'(0) = 1 \) to determine the values of \( A \) and \( B \). What is the general solution?
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