Solve the Initial Value Problem A) $y = 6 t ^ { 2 } + e ^ { - t } - 5 t - 1 - \frac { 2 } { e }$

question 9

Multiple Choice

Solve the initial value problem.
- $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm { dt } ^ { 2 } } = 6 - \mathrm { e } ^ { - \mathrm { t } } , \mathrm { y } ( 1 ) = \frac { - 1 } { \mathrm { e } } , \mathrm { y } ^ { \prime } ( 0 ) = - 4$$

• A) \(y = 6 t ^ { 2 } + e ^ { - t } - 5 t - 1 - \frac { 2 } { e }\)
• B) \(y = 3 t ^ { 2 } - e ^ { - t }\)
• C) \(y = 3 t ^ { 2 } - e ^ { - t } - 4 t\)
• D) \(y = 3 t ^ { 2 } - e ^ { - t } - 5 t + 2\)

---

Definitions:

Organic Compound

A chemical compound containing carbon atoms covalently bonded to other elements, typically hydrogen, oxygen, and nitrogen, among others.

Hydrocarbon Alkyne

A type of hydrocarbon that contains at least one carbon-carbon triple bond, part of the alkyne class of organic compounds.

Carbon Atoms

The fundamental building blocks of organic molecules, known for forming a vast number of compounds due to their ability to form stable bonds with themselves and other elements.

Supramolecular Polymers

Large structures formed from the non-covalent joining of monomers, characterized by interactions such as hydrogen bonding or van der Waals forces.