$\text { Use } u ( x , y ) = x ^ { 3 } y \text { as a integrating factor to find the general solution of the }$

question 78

Multiple Choice

$\text { Use } u ( x , y ) = x ^ { 3 } y \text { as a integrating factor to find the general solution of the }$ differential equation $\left( 4 y ^ { 3 } + 7 x ^ { 3 } y \right) d x + \left( 4 x y ^ { 2 } + 2 x ^ { 4 } \right) d y = 0$

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

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Definitions:

Substance

A form of matter that has a specific chemical composition and distinct physical properties.

Electrons

Subatomic particles with a negative charge, found orbiting the nucleus of an atom, involved in chemical bonds and electrical conductivity.

Enthalpy

A thermodynamic quantity equivalent to the total heat content of a system, representing the amount of energy needed to create a system plus the work needed to make room for it in its environment.

Free Energy

A thermodynamic quantity that represents the amount of work that can be performed by a system at a constant temperature and pressure.