For the Differential Equation, Find the Particular Solution $y = 0$

question 31

Multiple Choice

For the differential equation, find the particular solution $y = 0$ when $x = 0$ . $\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 3 } - 14 x$

• A) \(y = x ^ { 4 } - 14 x ^ { 2 }\)
• B) \(y = \frac { x ^ { 4 } } { 4 } - 7 x ^ { 2 }\)
• C) \(y = \frac { x ^ { 4 } } { 4 } + 7 x ^ { 2 }\)
• D) \(y = 4 x ^ { 4 } + 7 x ^ { 2 }\)
• E) \(y = \frac { x ^ { 4 } } { 2 } - 7 x\)

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Definitions:

Marginal Rate

The additional cost or benefit associated with a small unit change in a variable or activity.

Indifference Curve

A graph representing combinations of two goods that provide the consumer with the same level of satisfaction, illustrating preferences.

Constant

A value that does not change in mathematical expressions or economic models, acting as a fixed point of reference.

Diminishing

A principle indicating that as more of a good or service is consumed, the marginal benefit to the consumer decreases.