Two Linearly Independent Solutions of the Differential Equation $y ^ { \prime \prime } - 4 y ^ { \prime } + 5 y = 0$

question 35

Multiple Choice

Two linearly independent solutions of the differential equation $y ^ { \prime \prime } - 4 y ^ { \prime } + 5 y = 0$ are

• A) \(y _ { 1 } = e ^ { x } , y _ { 2 } = e ^ { 5 x }\)
• B) \(y _ { 1 } = e ^ { - x } , y _ { 2 } = e ^ { - 5 x }\)
• C) \(y _ { 1 } = e ^ { 2 x } \cos x , y _ { 2 } = e ^ { 2 x } \sin x\)
• D) \(y _ { 1 } = e ^ { x } \cos ( 2 x ) , y _ { 2 } = e ^ { x } \sin ( 2 x )\)
• E) \(y _ { 1 } = e ^ { - x } \cos ( 2 x ) , y _ { 2 } = e ^ { - 2 x } \sin ( 2 x )\)

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Definitions:

Temporal Bone

A pair of bones situated at the sides and base of the skull, contributing to the skull's structure and housing the organs of hearing and equilibrium.

Sphenoid Bone

A complex, butterfly-shaped bone at the base of the skull, which forms part of the eye socket, the nasal cavity, and the floor of the cranium.

Temporal Bone

A bone situated at the sides and base of the skull, containing the structures of the ear.

Sternum

A flat bone located in the center of the chest, serving as a major attachment point for ribs and protecting vital chest organs.