Solve the Problem $\frac { \mathrm { dx } } { \mathrm { dt } } = ( - 4 + 5 \mathrm { y } ) \mathrm { x }$

question 21

Multiple Choice

Solve the problem.
-The system of equations $\frac { \mathrm { dx } } { \mathrm { dt } } = ( - 4 + 5 \mathrm { y } ) \mathrm { x }$ and $\frac { \mathrm { dy } } { \mathrm { dt } } = ( - 4 + \mathrm { x } ) \mathrm { y }$ describes the growth rates of two symbiotic (dependent) species of animals (such as the rhinoceros and a type of bird which eats insects from its back) . Find the equilibrium points.

• A) \(( x , y ) = ( 0,0 )\) and \(( x , y ) = \left( 4 , \frac { 5 } { 4 } \right)\)
• B) \(( x , y ) = ( 0,0 )\) and \(( x , y ) = \left( - 4 , - \frac { 4 } { 5 } \right)\)
• C) \(( x , y ) = ( 0,0 )\) and \(( x , y ) = \left( 4 , \frac { 4 } { 5 } \right)\)
• D) \(( x , y ) = \left( 4 , \frac { 4 } { 5 } \right)\)

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