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Solve y'- 8ry = 2r. We will first find the solution y1 to the complementary equation, and then use variation of parameters to get the general solution. The complementary equation is y'+ which has the solution (use 0 for the constant of integration) Y1 = %3D You should think about why we can get away with letting the constant of integration be 0 here. The method of variation of parameters says to make the substitution y uY1. Substituting this into the original differential equation yields (write all expressions in terms of r) Solving this differential equation for u' gives (use c for the constant of integration) Therefore, the final answer is y = Question Help: O Message instructor Submit Oue

Solve y'- 8ry = 2r. We will first find the solution y1 to the complementary equation, and then use variation of parameters to get the general solution. The complementary equation is y'+ which has the solution (use 0 for the constant of integration) Y1 = %3D You should think about why we can get away with letting the constant of integration be 0 here. The method of variation of parameters says to make the substitution y uY1. Substituting this into the original differential equation yields (write all expressions in terms of r) Solving this differential equation for u' gives (use c for the constant of integration) Therefore, the final answer is y = Question Help: O Message instructor Submit Oue

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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Solve y'- 8ry = 2r. We will first find the solution y, to the complementary equation, and then use variation of parameters to get the general solution. The complementary equation is y'+ which has the solution (use 0 for the constant of integration) You should think about why we can get away with letting the constant of integration be 0 here. The method of variation of parameters says to make the substitution y original differential equation yields (write all expressions in terms of r) uy1. Substituting this into the Solving this differential equation for u' gives (use c for the constant of integration) Therefore, the final answer is Question Help: Message instructor Submit Question Esc F1 F2 F3 F4 F5 F6 F8 团
Transcribed Image Text:Solve y'- 8ry = 2r. We will first find the solution y, to the complementary equation, and then use variation of parameters to get the general solution. The complementary equation is y'+ which has the solution (use 0 for the constant of integration) You should think about why we can get away with letting the constant of integration be 0 here. The method of variation of parameters says to make the substitution y original differential equation yields (write all expressions in terms of r) uy1. Substituting this into the Solving this differential equation for u' gives (use c for the constant of integration) Therefore, the final answer is Question Help: Message instructor Submit Question Esc F1 F2 F3 F4 F5 F6 F8 团
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