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

Find the solution of the initial-value problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$ , $y ( 0 ) = 3$ .

A) $y = 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C$
B) $y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C }$
C) $y = 3 \ln \left( 1 + t ^ { 2 } \right) + 9$
D) $y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 9 }$
E) $y = 3 \ln \left( 1 + t ^ { 2 } \right) + 27$
F) $y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 27 }$
G) $y = 3 \ln \left( 1 + t ^ { 2 } \right)$
H) $y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) }$

Correct Answer:

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