Consider the system of ODEs \[\dfrac{dx}{dt} = x + y, \qquad \dfrac{dy}{dt} = y\] The general solution of this system of equations is单项选择题

题目图片
A

a. \( x = A e^t \) and \( y = B e^t \) where \( A \) and \( B \) are arbitrary constants

B

b. \( x = 0 \) and \( y = B e^t \) where \( B \) is an arbitrary constant

C

c. \( x = A \) and \( y = B e^t \) where \( A \) and \( B \) are arbitrary constants

D

d. None of the answers above

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