Solve Round Your Results to Four Decimal Places $\mathrm { dx } = 0.2$

Solve. Round your results to four decimal places.
-Use the Euler method with $\mathrm { dx } = 0.2$ to estimate $\mathrm { y } ( 3 )$ if $\mathrm { y } ^ { \prime } = - \mathrm { y }$ and $\mathrm { y } ( 2 ) = 2$ . What is the exact value of $\mathrm { y } ( 3 )$ ?

A) $\mathrm { y } \approx 0.4554$ , exact value is $\mathrm { e } ^ { - 2 }$
B) $\mathrm { y } \approx 0.2554$ , exact value is -e
C) $\mathrm { y } \approx 0.0554$ , exact value is $- 2 \mathrm { e }$
D) $\mathrm { y } \approx 0.6554$ , exact value is $2 \mathrm { e } ^ { - 1 }$