Just as there are simultaneous algebraic equations (where a pair of numbers have

Question

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.

y1=2/5y1−2/3y2y2=−2/3y1+2/5y2

A. y1=sin(x)+cos(x)y2=cos(x)−sin(x)

B. y1=e^−x y2=e^−x

C. y1=e^x y2=e^x

D. y1=e^4x y2=−e^4x

E. y1=cos(x) y2=−sin(x)

F. y1=2e^2x y2=3e^−2x

G. y1=sin(x) y2=cos(x)

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.

Explanation / Answer

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