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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 1CR
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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.
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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