Solve the Differential Equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$

question 21

Multiple Choice

Solve the differential equation $y ^ {tt} - 6 y ^ { t } + 9 y = 8 x ^ { 2 } e ^ { 3 x } \text { by the method of variation of }$ parameters.

• A) \(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 2 } { 3 } x ^ { 4 } \right) e ^ { 3 x }\)
• B) \(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 8 } { 15 } x ^ { 4 } \right) e ^ { 3 x }\)
• C)\(y = \left( C _ { 1 } + C _ { 2 } x + \frac { 4 } { 9 } x ^ { 2 } \right) e ^ { 3 x }\)
• D)\(y = \left( C _ { 1 } + C _ { 2 } x - \frac { 8 } { 17 } x ^ { 2 } \right) e ^ { 3 x }\)
• E)\(y = \left( C _ { 1 } + C _ { 2 } x - \frac { 4 } { 5 } x ^ { 2 } \right) e ^ { 3 x }\)

Know the global impact of declarations of independence following the American example.

Appreciate the role of persuasive writings in shaping public opinion and policy during the Revolutionary period.

Understand the significance of the Declaration of Independence and its legacy in inspiring future revolutions.

Identify the reasons behind the success or failure of military campaigns during the Revolutionary War.

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