For the Differential Equation, Find the Particular Solution If $y ( 5 ) = \frac { 1 } { 5 }$

question 46

Multiple Choice

For the differential equation, find the particular solution if $y ( 5 ) = \frac { 1 } { 5 }$ . $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x y ^ { 2 } } { x ^ { 2 } + 8 }$

• A) \(y = - \ln \left( x ^ { 2 } + 8 \right) - 5 - \frac { \ln 33 } { 2 }\)
• B) \(y = - \ln \left( x ^ { 2 } - 8 \right) - 5 - \frac { \ln 33 } { 2 }\)
• C) \(y = \frac { 2 } { \ln \left( 2 x ^ { 2 } + 8 \right) - 5 - \ln 33 }\)
• D) \(y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 5 }\)
• E) \(y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 10 - \ln 33 }\)

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Definitions:

Compounded Semi-annually

A method of calculating interest where the interest amount is added to the principal amount twice a year, leading to compound growth.

Amortization Period

The length of time it takes to fully pay off a debt with regular payments that cover both principal and interest.

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A type of mortgage where the borrower receives a cash rebate upfront, often used for home improvements or debt consolidation.

Compounded Semi-annually

A method of calculating interest where the interest is added to the principal amount twice a year and then interest is subsequently earned on the new principal.