Use Power Series to Solve the Differential Equation $$y ^ { t } = 4 x y .$$

question 3

Multiple Choice

Use power series to solve the differential equation. $$y ^ { t } = 4 x y .$$

• A)\(y ( x ) = c e ^ { - \frac { 4 x ^ { 2 } } { 2 } }\)
• B) \(y ( x ) = c e ^ { \frac { 4 x ^ { 2 } } { 2 } }\)
• C) \(y ( x ) = e ^ { - \frac { x ^ { 2 } } { 2 } }\)
• D) \(y ( x ) = c e ^ { 4 x }\)
• E)\(y ( x ) = 4 e ^ { \frac { x ^ { 2 } } { 2 } }\)

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Definitions:

Multiplication

An arithmetic process that involves multiplying two numbers to achieve their resultant multiplication.

Evaluate

To determine or calculate the value of something.

Exponentiation

The mathematical operation involving the raising of one number to the power of another.

Division

A mathematics operation where a number is divided into parts or segments, represented by the division sign (/ or ÷).