Answer B and C This problem is related to Problems 7.10-7.18 in the text. Instructions for forms of answers in differential equation problems: For second order DEs, the roots of the characteristic equation may be real or complex. If the roots are real, the complementary solution is the weighted sum of real exponentials. Use C1 and C2 for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the constant and Phi for the phase. All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" + 17y' + 72y= 7cos(9t+ 0.785398)u(t). a. Find the functional form of the complementary solution, y(t). Ye(t)=C1e^(-8t)+C2e^(-9) b. Find the particular solution, y,(t). Yp(t) = 0.097 help (formulas) help (formulas) c. Find the total solution, y(t) for the initial condition y(0) = 9 and y'(0) = 14. y(t) = help (formulas) Note the answers are checked to an absolute accuracy of 0.01.
Answer B and C This problem is related to Problems 7.10-7.18 in the text. Instructions for forms of answers in differential equation problems: For second order DEs, the roots of the characteristic equation may be real or complex. If the roots are real, the complementary solution is the weighted sum of real exponentials. Use C1 and C2 for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the constant and Phi for the phase. All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" + 17y' + 72y= 7cos(9t+ 0.785398)u(t). a. Find the functional form of the complementary solution, y(t). Ye(t)=C1e^(-8t)+C2e^(-9) b. Find the particular solution, y,(t). Yp(t) = 0.097 help (formulas) help (formulas) c. Find the total solution, y(t) for the initial condition y(0) = 9 and y'(0) = 14. y(t) = help (formulas) Note the answers are checked to an absolute accuracy of 0.01.
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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Transcribed Image Text:Answer B and C
This problem is related to Problems 7.10-7.18 in the text.
Instructions for forms of answers in differential equation problems:
For second order DEs, the roots of the characteristic equation may be real or complex. If the roots are real, the complementary solution is the weighted sum of real
exponentials. Use C1 and C2 for the weights, where C1 is associated with the root with smaller magnitude. If the roots are complex, the complementary solution is
the weighted sum of complex conjugate exponentials, which can be written as a constant times a decaying exponential times a cosine with phase. Use C1 for the
constant and Phi for the phase.
All numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation y" + 17y' + 72y = 7cos(9t+ 0.785398)u(t).
a. Find the functional form of the complementary solution, y(t).
Ye(t)=C1e^(-8t)+C2e^(-9)
b. Find the particular solution, y,(t).
Yp(t) = 0.097
help (formulas)
help (formulas)
c. Find the total solution, y(t) for the initial condition y(0) = 9 and y'(0) = 14.
y(t) =
help (formulas)
Note the answers are checked to an absolute accuracy of 0.01.
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