Solve the Differential Equation $y ^ {tt } + 5 y ^ { t } - 6 y = 7 \cos 2 x \text {, where }$

question 23

Multiple Choice

Solve the differential equation $y ^ {tt } + 5 y ^ { t } - 6 y = 7 \cos 2 x \text {, where }$ $y ( 0 ) = - 1$ and $y ^ {t } ( 0 ) = 6$ by the method of undetermined coefficients.

• A) \(y = \frac { 1 } { 5 } e ^ { x } - \frac { 81 } { 70 } e ^ { - 6 x } - \frac { 7 } { 25 } \cos 2 x + \frac { 7 } { 20 } \sin 2 x\)
• B) \(y = \frac { 7 } { 33 } e ^ { x } - \frac { 23 } { 20 } e ^ { - 6 x } + \frac { 7 } { 20 } \cos 2 x - \frac { 7 } { 20 } \sin 2 x\)
• C)\(y = - \frac { 53 } { 35 } e ^ { - x } + \frac { 121 } { 140 } e ^ { 6 x } - \frac { 7 } { 20 } \cos 2 x - \frac { 7 } { 20 } \sin 2 x\)
• D)\(y = \frac { 1 } { 5 } e ^ { x } - \frac { 23 } { 20 } e ^ { - 6 x } + \frac { 7 } { 20 } \cos 2 x - \frac { 7 } { 20 } \sin 2 x\)
• E)\(y = \frac { 1 } { 5 } e ^ { x } - \frac { 17 } { 20 } e ^ { - 6 x } - \frac { 7 } { 20 } \cos 2 x + \frac { 7 } { 20 } \sin 2 x\)

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Definitions:

I-Beam Frame Rail

A structural component in the chassis of vehicles and equipment characterized by its I-shaped cross-section, offering strength and rigidity.

C-Channel Frame Rail

A type of structural frame rail with a C-shaped cross section, often used in the construction of vehicle chassis for added strength.

RBM Value

The measure of Resilience-Based Management value, indicating the strength and resilience of a system or component, often used in engineering contexts.

Ultimate Rigidity

The maximum stiffness of a material or structure, representing its resistance to deformation under load.