In the Previous Problem, Apply the Laplace Transform $U ( x , s ) = \mathcal { L } \{ u ( x , t ) \}$

question 23

Multiple Choice

In the previous problem, apply the Laplace transform. The resulting equation for $U ( x , s ) = \mathcal { L } \{ u ( x , t ) \}$ is

• A) \(\frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } + s ^ { 2 } U = - s f ( x )\)
• B) \(\frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } + s ^ { 2 } U = f ( x )\)
• C) \(\frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = - f ( x )\)
• D) \(\frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = s f ( x )\)
• E) \(\frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = - s f ( x )\)

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Definitions:

Empirical Formula

The simplest expression of a compound's composition, showing the relative numbers of atoms of each type without structural information.

Br2

Bromine, a diatomic molecule consisting of two bromine atoms, used as a reagent in various chemical reactions.

Dimethylsulfide

An organic sulfur compound with the formula (CH3)2S, known for its distinctive smell reminiscent of the ocean or cooked corn.

Alkene

A hydrocarbon that contains at least one carbon-carbon double bond in its structure.