The Solution of the Equation for the Differential Equation $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } + y = 0$

question 19

Multiple Choice

The solution of the equation for the differential equation $x ^ { 2 } y ^ { \prime \prime } + 3 x y ^ { \prime } + y = 0$ is

• A) \(y = c _ { 1 } x ^ { - 1 } + c _ { 2 } x ^ { - 1 } \ln x\)
• B) \(y = c _ { 1 } x ^ { - 1 } + c _ { 2 } x ^ { - 2 }\)
• C) \(y = c _ { 1 } x ^ { ( - 3 + \sqrt { 5 } ) / 2 } + c _ { 2 } x ^ { ( - 3 - \sqrt { 5 } ) / 2 }\)
• D) \(y = c _ { 1 } x + c _ { 2 } x \ln x\)
• E) \(y = c _ { 1 } x + c _ { 2 } x ^ { 2 }\)

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Definitions:

Calorie

A unit of energy often used to quantify the amount of energy food provides to the human body.

Van der Waals Interaction

A weak force of attraction between molecules or parts of molecules that results from transient fluctuating electrical charges.

Hydrogen Bond

A weak chemical bond formed between the hydrogen atom of one molecule and an electronegative atom (often oxygen or nitrogen) of another molecule.

Ionic Bond

A chemical bond formed between two ions with opposite charges through the transfer of one or more electrons from one atom to the other.