Since Δ t = 1 8 {\displaystyle \Delta t={\frac {1}{8}}} , we have
t 0 = 0 , t 1 = 1 8 , t 2 = 2 8 , . . . {\displaystyle t_{0}=0,t_{1}={\frac {1}{8}},t_{2}={\frac {2}{8}},...} , so the question is asking for y ( t 1 ) = y 1 {\displaystyle y(t_{1})=y_{1}} ,
By Euler's formula we have then
y 1 = y 0 + f ( y 0 ) ⋅ Δ t = 2 + ( 1 − 2 ( 2 ) ) ⋅ 1 8 = 2 − 3 8 ⇒ y ( 1 8 ) = 13 8 {\displaystyle y_{1}=y_{0}+f(y_{0})\cdot \Delta t=2+(1-2(2))\cdot {\frac {1}{8}}=2-{\frac {3}{8}}\Rightarrow \color {blue}y\left({\frac {1}{8}}\right)={\frac {13}{8}}}
, we have
, so the question is asking for 
,
