Solve the Differential Equation $144 y ^ {tt} - 24 y ^ { t } + y = 12 \left( x + e ^ { x } \right) \text { by the method of }$

question 12

Multiple Choice

Solve the differential equation $144 y ^ {tt} - 24 y ^ { t } + y = 12 \left( x + e ^ { x } \right) \text { by the method of }$ undetermined coefficients.

• A) \(y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 2 x } + 288 + 12 x + \frac { 12 } { 121 } e ^ { x }\)
• B) \(y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 13 x + \frac { 12 } { 121 } e ^ { x }\)
• C)\(y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 5 x + \frac { 12 } { 121 } e ^ { x }\)
• D)\(y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 12 x } + 288 + 12 x + \frac { 12 } { 121 } e ^ { x }\)
• E)\(y = \left( C _ { 1 } + C _ { 2 } x \right) e ^ { 1 / 2 x } + 288 + 2 x + \frac { 12 } { 121 } e ^ { x }\)

---

Definitions:

Pulling Effort

The force required to move or tow something, often measured to ensure the adequacy of a vehicle's towing capacity.

Force

Push or pull effort measured in units of weight. Force represents the ability to do work but this ability does not necessarily result in any work done; for instance, you can push all you like on a tractor/trailer combination but it is unlikely to move the vehicle. The formula for force (F) is calculated by multiplying pressure (P) by the area (A) it acts on. F=P*A.

Perfect Vacuum

A theoretical state where a space is completely devoid of matter, including air or any other gases, achieving a total absence of pressure.

Sealed Vessel

A container designed to be completely airtight, preventing the exchange of substances with its environment.