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

question 71

Multiple Choice

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 = - \(\frac { 3 } { 2 t ^ { 2 } }\) + \(\frac { 1 } { 2 t }\)

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