$\text { Use } u ( x , y ) = x ^ { 4 } y \text { as a integrating factor to find the general solution of the }$

question 5

Multiple Choice

$\text { Use } u ( x , y ) = x ^ { 4 } y \text { as a integrating factor to find the general solution of the }$ differential equation $\left( 5 y ^ { 4 } + 8 x ^ { 3 } y \right) d x + \left( 5 x y ^ { 3 } + 2 x ^ { 4 } \right) d y = 0$

• A) \(x ^ { 4 } y ^ { 7 } + x ^ { 10 } y ^ { 2 } = C\)
• B) \(x ^ { 5 } y ^ { 5 } + x ^ { 8 } y ^ { 3 } = C\)
• C) \(x ^ { 5 } y ^ { 5 } + x ^ { 8 } y ^ { 2 } = C\)
• D) \(x ^ { 6 } y ^ { 4 } + x ^ { 9 } y ^ { 2 } = C\)
• E) \(x ^ { 6 } y ^ { 4 } + x ^ { 9 } y ^ { 3 } = C\)

---

Definitions:

Control Series Design

An extension of the interrupted time series quasi-experimental design in which there is a comparison or control group.

Interrupted Time Series

An analytical method that assesses the impact of an intervention on a time series of data points.

True Experimental

A type of experimental design that includes a control group and random assignment to groups to test the effect of an intervention.

Cohort

A group of people born at about the same time and exposed to the same societal events; cohort effects are confounded with age in a cross-sectional study.