Solve the Initial-Value Problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$

Multiple Choice

Solve the initial-value problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$ , $y ( 0 ) = 3$ . Then use your solution to evaluate $y ( \sqrt { e - 1 } )$ .

A) $\sqrt [ 3 ] { 30 }$
B) $\sqrt [ 3 ] { 12 }$
C) $30$
D) 1
E) $\sqrt [ 3 ] { 3 }$
F) $\sqrt [ 3 ] { 10 }$
G) 12
H) 27