For the Differential Equation, Find the Particular Solution If $y \left( \frac { 1 } { 7 } \right) = e ^ { 7 }$

Multiple Choice

For the differential equation, find the particular solution if $y \left( \frac { 1 } { 7 } \right) = e ^ { 7 }$ $x ^ { 2 } \frac { \mathrm { d } y } { \mathrm {~d} x } = y$

A) $y = e ^ { 14 - \frac { 1 } { x } }$
B) $y = e ^ { 14 - x }$
C) $y = e ^ { 14 + \frac { 1 } { x } }$
D) $y = 14 e ^ { - \frac { 1 } { x } }$
E) $y = e ^ { 1 - \frac { 14 } { x } }$