Which of the Following Is a Solution of the Differential $\frac { d ^ { 2 } y } { d x ^ { 2 } } - 6 \frac { d y } { d x } + 9 y = 0$

question 72

Multiple Choice

Which of the following is a solution of the differential equation $\frac { d ^ { 2 } y } { d x ^ { 2 } } - 6 \frac { d y } { d x } + 9 y = 0$

• A) \(y = e ^ { - 3 x }\)
• B) \(y = e ^ { 2 x }\)
• C) \(y = x e ^ { - 3 x }\)
• D) \(y = x e ^ { 3 x }\)
• E) \(y = e ^ { - 2 x }\)
• F) \(y = e ^ { - 3 x } + x\)
• G) \(y = x e ^ { 3 x } + x\)
• H)None of these

---

Definitions:

Tax-Exempt Income

Income that is not subject to tax by federal, state, or local authorities, allowing the recipient to keep the full amount.

Recognize Income

The process of reporting income when it is earned, according to accounting principles, regardless of when it is received.

Unemployment Compensation

Financial benefits provided to individuals who have lost their job through no fault of their own, as a means to temporarily assist them while they seek new employment.

Taxable

Relates to income, assets, or transactions that are subject to tax by governmental authorities.