Solve the Initial Value Problem $$\frac { d y } { d t } = e ^ { - t } \sec ^ { 2 } \left( \pi e ^ { - t } \right) , y ( - \ln 5 ) = \frac { 1 } { \pi }$$

question 129

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d t } = e ^ { - t } \sec ^ { 2 } \left( \pi e ^ { - t } \right) , y ( - \ln 5 ) = \frac { 1 } { \pi }$$

• A) \(y = \frac { \tan \left( \pi \mathrm { e } ^ { - \mathrm { t } } \right) + 6 } { \pi }\)
• B) \(y = \frac { - e ^ { - t } \cot \left( \pi e ^ { - t } \right) + 0 } { \pi }\)
• C) \(y = \cot \left( \pi e ^ { - t } \right) + 1\)
• D) \(y = \frac { - \tan \left( \pi e ^ { - t } \right) + 1 } { \pi }\)

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Definitions:

Personal Saving

The portion of an individual's income that is not spent on consumption or taxes and is set aside for future use or investment.

Loanable Funds Curve

A graphical representation of the market for loanable funds, showing the relationship between the interest rate and the quantity of loanable funds supplied and demanded.

Real Interest Rate

The interest rate adjusted for inflation, showing the true cost of borrowing or the real yield on an investment.

Saving

The portion of income not spent on consumption or taxes and is typically set aside for future use or emergencies.