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Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations). Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations. 3/₁ = y2 Y/2 A. y₁= sin(x) + cos(x) B. y₁ = cos(x) OC. y₁ = e4x Y2 = Y2 = 4x y2 = cos(x) sin(x) sin(x) - =-Y1

Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations). Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations. 3/₁ = y2 Y/2 A. y₁= sin(x) + cos(x) B. y₁ = cos(x) OC. y₁ = e4x Y2 = Y2 = 4x y2 = cos(x) sin(x) sin(x) - =-Y1

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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Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations). Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations. y₂ = -Y1 A. Y₁ = sin(x) + cos(x) Y1 B. y₁ = cos(x) 4x C. Y₁ = eª D. Y₁ = E. Y₁ = ex F. Y1 = ex G. Y₁ = sin(x) 2e-2x Y2 Y2 = =sin(x) = e4º Y2 = 3e-2x Y₂ = ex Y2 = cos(x) = sin(x) = Y2 = e ม่า Y₂ = cos(x) Y2 = Y2 As you can see, finding all of the solutions, particularly of a system of equations, can be complicated and time consuming. It helps greatly if we study the structure of the family of solutions to the equations. Then if we find a few solutions we will be able to predict the rest of the solutions using the structure of the family of solutions.
Transcribed Image Text:Just as there are simultaneous algebraic equations (where a pair of numbers have to satisfy a pair of equations) there are systems of differential equations, (where a pair of functions have to satisfy a pair of differential equations). Indicate which pairs of functions satisfy this system. It will take some time to make all of the calculations. y₂ = -Y1 A. Y₁ = sin(x) + cos(x) Y1 B. y₁ = cos(x) 4x C. Y₁ = eª D. Y₁ = E. Y₁ = ex F. Y1 = ex G. Y₁ = sin(x) 2e-2x Y2 Y2 = =sin(x) = e4º Y2 = 3e-2x Y₂ = ex Y2 = cos(x) = sin(x) = Y2 = e ม่า Y₂ = cos(x) Y2 = Y2 As you can see, finding all of the solutions, particularly of a system of equations, can be complicated and time consuming. It helps greatly if we study the structure of the family of solutions to the equations. Then if we find a few solutions we will be able to predict the rest of the solutions using the structure of the family of solutions.
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