Find the Particular Solution of the Differential Equation $\frac { 3 y } { x - 8 } d x + [ 3 \ln ( x - 8 ) + 10 y ] d y = 0$

question 18

Multiple Choice

Find the particular solution of the differential equation $\frac { 3 y } { x - 8 } d x + [ 3 \ln ( x - 8 ) + 10 y ] d y = 0$ that satisfies the initial condition $y ( 9 ) = 2$

• A) \(3 y \ln ( x - 8 ) + 5 y = 10\)
• B) \(3 y \ln ( x - 8 ) + 5 y ^ { 2 } = 20\)
• C) \(3 y ( x - 8 ) + 10 y = 26\)
• D) \(3 y \ln ( x - 8 ) + 10 y = 20\)
• E) \(\frac { 3 y } { ( x - 8 ) } + 5 y ^ { 2 } = 26\)

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Definitions:

Sporophyte

The diploid, spore-producing phase in the life cycle of a plant that alternates with the haploid gametophyte phase.

Ovule

A plant structure in seed plants that develops into a seed after fertilization, containing a female gametophyte and the egg cell.

Angiosperms

Flowering plants that produce seeds enclosed within a fruit, representing the most diverse group of land plants.

Fertilization

The fusion of male and female gametes to form a zygote, initiating the development of a new organism.