Find the Integrating Factor, the General Solution, and the Particular $y ^ { \prime }$

Find the integrating factor, the general solution, and the particular solution satisfying the initial condition. 2t $y ^ { \prime }$ - y = $\frac { 6 } { t }$ ; y(1) = -1, t > 0

A) integrating factor:\ $t ^ { - 1 / 2 }$
General solution: y = - $\frac { 2 } { t }$ + C $t ^ { 1 / 2 }$
Particular solution: y = - $\frac { 2 } { t }$ + $t ^ { 1 / 2 }$
B) integrating factor: 2t
General solution: y = - $\frac { 3 } { 4 t ^ { 2 } }$ + $\frac { C } { 2 t }$
Particular solution: y = - $\frac { 3 } { 4 t ^ { 2 } }$ + $\frac { 1 } { 4 t }$
C) integrating factor: $t ^ { - 1 / 2 }$
General solution: y = -4 + C $t ^ { 1 / 2 }$
Particular solution: y = -4 + 3 $t ^ { 1 / 2 }$
D) integrating factor: 2t
General solution: y = - $\frac { 3 } { 2 t ^ { 2 } }$ + $\frac { C } { 2 t }$
Particular solution: y = - $\frac { 3 } { 2 t ^ { 2 } }$ + $\frac { 1 } { 2 t }$

Correct Answer:

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