Solve the Initial Value Problem $$\frac { d y } { d t } = e ^ { - t } \sec ^ { 2 } \left( \pi e ^ { - t } \right) , y ( - \ln 1 ) = \frac { 7 } { \pi }$$

question 61

Multiple Choice

Solve the initial value problem.
- $$\frac { d y } { d t } = e ^ { - t } \sec ^ { 2 } \left( \pi e ^ { - t } \right) , y ( - \ln 1 ) = \frac { 7 } { \pi }$$

• A) \(y = \cot \left( \pi \mathrm { e } ^ { - \mathrm { t } } \right) + 7\)
• B) \(y = \frac { - \tan \left( \pi \mathrm { e } ^ { - \mathrm { t } } \right) + 7 } { \pi }\)
• C) \(y = \frac { \tan \left( \pi \mathrm { e } ^ { - \mathrm { t } } \right) + 8 } { \pi }\)
• D) \(\mathrm { y } = \frac { - \mathrm { e } ^ { - \mathrm { t } } \cot \left( \pi \mathrm { e } ^ { - \mathrm { t } } \right) + 6 } { \pi }\)

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