Solve the Differential Equation Using the Method of Undetermined Coefficients $$y ^ { tt } + 6 y ^ { t } + 9 y = 2 + x$$

question 121

Multiple Choice

Solve the differential equation using the method of undetermined coefficients.
$$y ^ { tt } + 6 y ^ { t } + 9 y = 2 + x$$
Select the correct answer.

• A) \(y ( x ) = c _ { 1 } x e ^ { - 3 x } + c _ { 2 } x ^ { 2 } e ^ { - 3 x } + \frac { 4 } { 27 } x\)
• B) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x } + \frac { 1 } { 9 } x + \frac { 4 } { 27 }\)
• C) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x }\)
• D) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + \frac { 1 } { 9 } x + \frac { 4 } { 27 }\)
• E) \(y ( x ) = c _ { 1 } e ^ { - 3 x } + c _ { 2 } x e ^ { - 3 x } + \frac { 2 } { 9 } x\)

Differentiate between tectonic settings and their associated features such as fold and thrust belts, foreland basins, and accretionary prisms.

Understand the geological significance of basins in various tectonic settings and their formation mechanisms.

Grasp the complexities of fault movements and their implications on crustal deformation and basin development.

Evaluate the contribution of subduction processes, including the formation of accretionary prisms and volcanic arcs, to regional geology.

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