Solve the Differential Equation $y ^ { tt } + 2 y ^ { t } = 4 e ^ { x } \text { by the method of undetermined }$

question 29

Multiple Choice

Solve the differential equation $y ^ { tt } + 2 y ^ { t } = 4 e ^ { x } \text { by the method of undetermined }$ coefficients.

• A)\(y = C _ { 1 } + C _ { 2 } e ^ { 3 x } + \frac { 4 } { 3 } e ^ { x }\)
• B)\(y = C _ { 1 } + C _ { 2 } e ^ { - 3 x } - \frac { 4 } { 3 } e ^ { x }\)
• C)\(y = C _ { 1 } + C _ { 2 } e ^ { - 2 x } + \frac { 4 } { 3 } e ^ { x }\)
• D) \(y = C _ { 1 } + C _ { 2 } e ^ { 3 x } - 3 e ^ { x }\)
• E) \(y = C _ { 1 } + C _ { 2 } e ^ { - 2 x } + 4 e ^ { x }\)

---

Definitions:

Human Nature

The inherent characteristics, feelings, and behavioral traits shared by all humans.

Libido

A term used in psychoanalytic theory to denote the energy of the sexual drive.

Neurosis

Describes a class of functional mental disorders involving chronic distress but neither delusions nor hallucinations, making it difficult to cope with life.

Hypnosis

A trance-like state of focused attention and increased suggestibility, often used for therapeutic purposes.