The Solution Of $y ^ { \prime \prime } + 3 y ^ { \prime } - 4 y = \cos x$

question 16

Multiple Choice

The solution of $y ^ { \prime \prime } + 3 y ^ { \prime } - 4 y = \cos x$ is

• A) \(y = c _ { 1 } e ^ { x } + c _ { 2 } e ^ { - 4 x } + ( 5 \sin x + 3 \cos x ) / 34\)
• B) \(y = c _ { 1 } e ^ { x } + c _ { 2 } e ^ { - 4 x } + ( - 5 \sin x + 3 \cos x ) / 34\)
• C) \(y = c _ { 1 } e ^ { x } + c _ { 2 } e ^ { - 4 x } + ( - 5 \cos x - 3 \sin x ) / 34\)
• D) \(y = c _ { 1 } e ^ { x } + c _ { 2 } e ^ { - 4 x } + ( 5 \cos x + 3 \sin x ) / 34\)
• E) \(y = c _ { 1 } e ^ { x } + c _ { 2 } e ^ { - 4 x } + ( - 5 \cos x + 3 \sin x ) / 34\)

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Definitions:

Benthic

Related to the bottom of a sea or lake or to the organisms that live on or in the bottom sediments.

Pelagic

Referring to oceanic water not close to the bottom or shore, encompassing the entire water column used particularly in context to the life and ecosystems found within this vast, open ocean area.

Biodiversity

The variety and variability of life forms within a given ecosystem, region, or the entire Earth, crucial for maintaining ecological balance.

Trawl Fishing

A method of fishing that involves dragging a large net through the water, either at midwater or along the sea bottom.