$\text { Find the particular solution of the differential equation } \frac { d y } { d x } + 7 x ^ { 3 } y = x ^ { 3 } \text { passing }$

question 77

Multiple Choice

$\text { Find the particular solution of the differential equation } \frac { d y } { d x } + 7 x ^ { 3 } y = x ^ { 3 } \text { passing }$ through the point $\left( 0 , \frac { 3 } { 2 } \right)$ .

• A) \(y = \frac { 1 } { 14 } - \frac { 23 } { 14 } e ^ { - 1.75 x ^ { 4 } }\)
• B) \(y = \frac { 1 } { 7 } + \frac { 5 } { 14 } e ^ { - 1.75 x ^ { 4 } }\)
• C) \(y = \frac { 1 } { 7 } + \frac { 23 } { 14 } e ^ { - 1.75 x ^ { 4 } }\)
• D) \(y = \frac { 1 } { 7 } + \frac { 19 } { 14 } e ^ { - 1.75 x ^ { 4 } }\)
• E) \(y = \frac { 1 } { 14 } - \frac { 19 } { 14 } e ^ { - 1.75 x ^ { 4 } }\)

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Definitions:

Significance Level

The probability of rejecting the null hypothesis in a statistical test when it is true, commonly set at 0.05 or 5%.

Chi-Square Value

A statistic that measures the difference between observed and expected frequencies to test for independence in categorical variables.

Null Hypothesis

A hypothesis used in statistical testing that assumes no significant difference or effect exists between certain states or variables.

Observed Frequency

The number of times a particular value or category of data occurs in a set of data, used in the analysis of categorical variables.