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a) Which of the following ODE is an initial value problem (IVP) of 2nd-order linear ODE ? OlI, where I:y" – 5y' = -6y, y(1) = 2, y'(0) = 5 II:y" – 5y' = -6y, y(2) = 1, y'(2) = 3, III:y" – 5y' = -6y, y(5) = 1, y' (3) = 7. b) Is the ODE of the IVP in point a) homogeneous? How would you continue to solve this IVP? ONo, it is not homogenous because it has terms in the right hand side of the ODE. OYes, it is homogenous. As the ODE has constant coefficients, we can solve the characteristic equation in order to find the general solution. Then imposing the initial conditions we can get the solution to the IVP. OYes, it is homogenous, but the ODE doesn't have constant coefficients. We need first to reduce this ODE to an ODE with constant coefficients, then we nèed to solve the characteristic equation to find the general solution. Finally, we need to use the initial conditions to solve the IVP.

a) Which of the following ODE is an initial value problem (IVP) of 2nd-order linear ODE ? OlI, where I:y" – 5y' = -6y, y(1) = 2, y'(0) = 5 II:y" – 5y' = -6y, y(2) = 1, y'(2) = 3, III:y" – 5y' = -6y, y(5) = 1, y' (3) = 7. b) Is the ODE of the IVP in point a) homogeneous? How would you continue to solve this IVP? ONo, it is not homogenous because it has terms in the right hand side of the ODE. OYes, it is homogenous. As the ODE has constant coefficients, we can solve the characteristic equation in order to find the general solution. Then imposing the initial conditions we can get the solution to the IVP. OYes, it is homogenous, but the ODE doesn't have constant coefficients. We need first to reduce this ODE to an ODE with constant coefficients, then we nèed to solve the characteristic equation to find the general solution. Finally, we need to use the initial conditions to solve the IVP.

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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a) Which of the following ODE is an initial value problem (IVP) of 2nd-order linear ODE ? Oill, where I:y" – 5y' = -6y, y(1) = 2, y' (0) = 5 II:y" – 5y' =-6y, y(2) = = 3, III:y" – 5y' = -6y, y(5) = 1, y' (3) = 7. b) Is the ODE of the IVP in point a) homogeneous? How would you continue to solve this IVP? 1, y'(2) ONo, it is not homogenous because it has terms in the right hand side of the ODE. OYes, it is homogenous. As the ODE has constant coefficients, we can solve the characteristic equation in order to find the general solution. Then imposing the initial conditions we can get the solution to the IVP. OYes, it is homogenous, but the ODE doesn't have constant coefficients. We need first to reduce this ODE to an ODE with constant coefficients, then we nèed to solve the characteristic equation to find the general solution. Finally, we need to use the initial conditions to solve the IVP.
Transcribed Image Text:a) Which of the following ODE is an initial value problem (IVP) of 2nd-order linear ODE ? Oill, where I:y" – 5y' = -6y, y(1) = 2, y' (0) = 5 II:y" – 5y' =-6y, y(2) = = 3, III:y" – 5y' = -6y, y(5) = 1, y' (3) = 7. b) Is the ODE of the IVP in point a) homogeneous? How would you continue to solve this IVP? 1, y'(2) ONo, it is not homogenous because it has terms in the right hand side of the ODE. OYes, it is homogenous. As the ODE has constant coefficients, we can solve the characteristic equation in order to find the general solution. Then imposing the initial conditions we can get the solution to the IVP. OYes, it is homogenous, but the ODE doesn't have constant coefficients. We need first to reduce this ODE to an ODE with constant coefficients, then we nèed to solve the characteristic equation to find the general solution. Finally, we need to use the initial conditions to solve the IVP.
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