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For 3 given solutions of a second order, linear and homogeneous ODE not any linear combination of them is a solution of the same ODE their difference is not a solution of the same ODE their product is a solution of the same ODE their sum is a solution of the same ODE O it is a wrong question: a second order ODE can only have 2 linear independent solutions! their sum is a solution of another ODE O their derivatives are also solutions of the same ODE

For 3 given solutions of a second order, linear and homogeneous ODE not any linear combination of them is a solution of the same ODE their difference is not a solution of the same ODE their product is a solution of the same ODE their sum is a solution of the same ODE O it is a wrong question: a second order ODE can only have 2 linear independent solutions! their sum is a solution of another ODE O their derivatives are also solutions of the same ODE

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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For three given solutions of a second order, linear and homogeneous ODE: - ○ Not any linear combination of them is a solution of the same ODE - ○ Their difference is not a solution of the same ODE - ○ Their product is a solution of the same ODE - ○ Their sum is a solution of the same ODE - ○ It is a wrong question: a second order ODE can only have 2 linear independent solutions! - ○ Their sum is a solution of another ODE - ○ Their derivatives are also solutions of the same ODE
Transcribed Image Text:For three given solutions of a second order, linear and homogeneous ODE: - ○ Not any linear combination of them is a solution of the same ODE - ○ Their difference is not a solution of the same ODE - ○ Their product is a solution of the same ODE - ○ Their sum is a solution of the same ODE - ○ It is a wrong question: a second order ODE can only have 2 linear independent solutions! - ○ Their sum is a solution of another ODE - ○ Their derivatives are also solutions of the same ODE
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