Two Linearly Independent Solutions of the Differential Equation $y ^ { \prime \prime } - 6 y ^ { \prime } + 9 y = 0$

question 6

Multiple Choice

Two linearly independent solutions of the differential equation $y ^ { \prime \prime } - 6 y ^ { \prime } + 9 y = 0$ are

• A) \(y _ { 1 } = e ^ { 3 x } , y _ { 2 } = x e ^ { 3 x }\)
• B) \(y _ { 1 } = e ^ { - 3 x } , y _ { 2 } = x e ^ { - 3 x }\)
• C) \(y _ { 1 } = e ^ { 3 x } , y _ { 2 } = x e ^ { - 3 x }\)
• D) \(y _ { 1 } = e ^ { 3 x } \cos ( x ) , y _ { 2 } = x e ^ { 3 x } \sin ( x )\)
• E) \(y _ { 1 } = e ^ { - 3 x } \cos ( 3 x ) , y _ { 2 } = e ^ { - 3 x } \sin ( x )\)

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