Consider the differential equation and initial condition
d y d t = 2 − y 2 , y ( 0 ) = 1 {\displaystyle {\frac {dy}{dt}}=2-y^{2},\quad y(0)=1}
Use Euler's method with one step of size Δ t = 0.1 {\displaystyle \Delta t=0.1} to approximate the value of the solution at time t = 0.1 {\displaystyle t=0.1}
(a) y ( 0.1 ) = 2 {\displaystyle y(0.1)=2}
(b) y ( 0.1 ) = 2.1 {\displaystyle y(0.1)=2.1}
(c) y ( 0.1 ) = 2.2 {\displaystyle y(0.1)=2.2}
(d) y ( 0.1 ) = 1.2 {\displaystyle y(0.1)=1.2}
(e) y ( 0.1 ) = 1.1 {\displaystyle y(0.1)=1.1}
to approximate the value of the solution at time 
