When the Laplace Transform Is Applied to the Problem $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { 3 t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 2$

question 2

Multiple Choice

When the Laplace transform is applied to the problem $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { 3 t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 2$ the resulting transformed equation is

• A) \(\left( s ^ { 2 } + 2 s + 1 \right) Y = - s - 4 + 1 / ( s - 3 )\)
• B) \(\left( s ^ { 2 } + 2 s + 1 \right) Y = s - 4 + 1 / ( s - 3 )\)
• C) \(\left( s ^ { 2 } + 2 s + 1 \right) Y = s + 4 + 1 / ( s + 3 )\)
• D) \(\left( s ^ { 2 } + 2 s + 1 \right) Y = - s - 4 + 1 / ( s + 3 )\)
• E) \(\left( s ^ { 2 } + 2 s + 1 \right) Y = s + 4 + 1 / ( s - 3 )\)

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Definitions:

Neutral Alleles

Genetic variants that do not affect the fitness of an organism and are unaffected by natural selection.

Population Size

The total number of individual organisms inhabiting a particular area or environment at a given time.

Inbreeding

The mating of closely related individuals, which can increase the chance of offspring inheriting identical copies of genes from both parents, potentially leading to a greater risk of recessive genetic disorders.

Deleterious Alleles

Deleterious alleles are variants of genes that negatively affect the fitness or survival of an individual carrying them.