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2) The objective of this question is the transformation of a 2nd order finear differential equation into a system of 2 ordinary differential equations. Consider the following linear differential equation (E) a" +4' + 3a = 0. and let us set: u= rand v= 2'. 1) What is the system of differential equations (S) satisfied by (u, v) when a satisfies (E) (and vice-versa)? 2) Solve (S) and deduce the general solution of (E). 3) Does the above results for (E) agree with the formulas of the general solutions of a 2nd order linear homogeneous differential equation with constant coefficients ?

2) The objective of this question is the transformation of a 2nd order finear differential equation into a system of 2 ordinary differential equations. Consider the following linear differential equation (E) a" +4' + 3a = 0. and let us set: u= rand v= 2'. 1) What is the system of differential equations (S) satisfied by (u, v) when a satisfies (E) (and vice-versa)? 2) Solve (S) and deduce the general solution of (E). 3) Does the above results for (E) agree with the formulas of the general solutions of a 2nd order linear homogeneous differential equation with constant coefficients ?

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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2) The objective of this question is the transformation of a 2nd order finear differential equation into a system of 2 ordinary differential equations. Consider the following linear differential equation (E) a" + 4 + 3 = 0. and let us set: @=r and v= 2'. 1) What is the system of differential equations (S) satisfied by (u, v) when a satisfies (E) (and vice-versa)? 2) Solve (S) and deduce the general solution of (E). 3) Does the above results for (E) agree with the formulas of the general solutions of a 2nd order linear homogeneous differential equation with constant coefficients ?
Transcribed Image Text:2) The objective of this question is the transformation of a 2nd order finear differential equation into a system of 2 ordinary differential equations. Consider the following linear differential equation (E) a" + 4 + 3 = 0. and let us set: @=r and v= 2'. 1) What is the system of differential equations (S) satisfied by (u, v) when a satisfies (E) (and vice-versa)? 2) Solve (S) and deduce the general solution of (E). 3) Does the above results for (E) agree with the formulas of the general solutions of a 2nd order linear homogeneous differential equation with constant coefficients ?
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