Solve the Boundary-Value Problem, If Possible $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

question 61

Multiple Choice

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

• A) \(y ( x ) = 4 x e ^ { ( - 8 x + 8 ) }\)
• B) \(y ( x ) = 4 e ^ { ( - 8 x - 8 ) }\)
• C) \(y ( x ) = 4 x e ^ { ( - 8 x - 8 ) }\)
• D) \(y ( x ) = 8 x e ^ { ( - 4 x + 4 ) }\)
• E) No solution

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Definitions:

CCC Bond Angle

Refers to the angle between three consecutive carbon atoms within a molecule, significant in determining the molecule's shape and reactivity.

Propene

A flammable hydrocarbon of the alkene series, consisting of three carbon atoms and six hydrogen atoms (C3H6).

Atomic Orbitals

Regions around an atom where there is a high probability of finding electrons, described by quantum numbers.

Hybrid Atomic Orbitals

Orbitals formed from the combination of two or more atomic orbitals on the same atom, leading to equivalent energy levels suitable for bonding.