Let F(t) Be the Solution Of $y ^ { \prime }$

Multiple Choice

Let f(t) be the solution of $y ^ { \prime }$ = $y ^ { 2 }$ t + y + $\mathrm { e } ^ { \mathrm { t } }$ , f(0) = 2. If Euler's method with n = 4 is used to approximate f(t) for $0 \leq t \leq 2$ find f $\left( \frac { 1 } { 2 } \right)$ .

A) 2(4 + $\sqrt { \mathrm { e } }$ )
B) $\frac { y ^ { 2 } } { 2 }$ + y + $e ^ { 1 / 2 }$
C) $\frac { 7 } { 2 }$
D) 3 + $e ^ { 2 }$
E) none of these