Solve the Differential Equation Using the Method of Undetermined Coefficients $$y ^ { tt } - 5 y ^ { t } = \sin 15 x$$

question 128

Multiple Choice

Solve the differential equation using the method of undetermined coefficients.
$$y ^ { tt } - 5 y ^ { t } = \sin 15 x$$

• A)
• \(y ( x ) = c _ { 1 } e ^ { 5 x } + \frac { 1 } { 250 } \cos ( 6 x ) + \frac { 1 } { 750 } \sin ( 6 x )\)
• B)
• \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 5 x } + \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)
• C)
• \(y ( x ) = c _ { 1 } + c _ { 2 } e ^ { 5 x } - \frac { 1 } { 250 } \sin ( 6 x )\)
• D)
• \(y ( x ) = c _ { 1 } e ^ { 5 x } + \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)
• E)
• \(y ( x ) = \frac { 1 } { 750 } \cos ( 6 x ) - \frac { 1 } { 250 } \sin ( 6 x )\)

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Definitions:

Income Statements

A financial statement that shows a company's revenues, expenses, and profits or losses over a particular period.

Trial Balance

An accounting report that lists all the balances of each ledger account to ensure that debits equal credits, used as a tool for checking the accuracy of bookkeeping entries.

T Accounts

A graphical representation used in accounting to show the effects of transactions on individual accounts.

Net Income

The total earnings of a company after subtracting all expenses, taxes, and losses.