Solve the Differential Equation $x ^ { 2 } \frac { d y } { d x } - y = 2 x ^ { 3 } e ^ { - 1 / x }$

question 26

Multiple Choice

Solve the differential equation. $x ^ { 2 } \frac { d y } { d x } - y = 2 x ^ { 3 } e ^ { - 1 / x }$

• A) \(y = C e ^ { - 2 / x }\)
• B) \(y = x ^ { 2 } e ^ { - 1 / x } + C e ^ { - 1 / x }\)
• C) \(y = C x e ^ { 2 x }\)
• D) \(y = e ^ { 1 / x } x + C e ^ { 1 / x }\)
• E) \(\text { none of these }\)

---

Definitions:

Hypoglossal

Relating to the hypoglossal nerve, which is the twelfth cranial nerve responsible for motor function of most of the tongue muscles.

Abducens

Relating to the abducens nerve, which is the sixth cranial nerve responsible for controlling the movement of a muscle that abducts the eyeball (lateral rectus muscle).

Medulla Oblongata

The lowest part of the brainstem, controlling vital body functions such as breathing, heart rate, and blood pressure.

Vestibule

An entrance or enclosed antechamber between the outside and the interior of a building or space.