The Particular Solution of the Differential Equation $\frac { d v } { d t } = 8 t + \csc ^ { 2 } t$

Multiple Choice

The particular solution of the differential equation $\frac { d v } { d t } = 8 t + \csc ^ { 2 } t$ satisfying the boundary condition $v \left( \frac { \pi } { 2 } \right) = - 7$ is

A) $v = 4 x ^ { 2 } - \cot t - 7 + \pi ^ { 2 }$
B) $v = 4 x ^ { 2 } + \cot t + 7 + \pi ^ { 2 }$
C) $v = 4 x ^ { 2 } + \cot t - 7 - \pi ^ { 2 }$
D) $v = 4 x ^ { 2 } - \cot t - 7 - \pi ^ { 2 }$
E) $v = 4 x ^ { 2 } - \cot t + 7 + \pi ^ { 2 }$