Which of the Following Systems Are Linear? Select All That $\frac { d x } { d t } = x + y , \frac { d y } { d t } = 2 t - 3 \sin t$

question 3

Multiple Choice

Which of the following systems are linear? Select all that apply.

• A) \(\frac { d x } { d t } = x + y , \frac { d y } { d t } = 2 t - 3 \sin t\)
• B) \(\frac { d x } { d t } = 3.5 x + 2 y , \frac { d y } { d t } = 2 x - 5 y\)
• C) \(\frac { d x } { d t } = x + 1 / y , \frac { d y } { d t } = 2 x e ^ { t } - 3 y\)
• D) \(\frac { d x } { d t } = 0 , \frac { d y } { d t } = 2 \cos x - 3 y\)
• E) \(\frac { d x } { d t } = t ^ { 2 } + 1 , \frac { d y } { d t } = 15 x - 4 y\)

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Definitions:

Voluntary Reorganization

A process initiated by a company to restructure its operations, finances, or organizational structure by choice rather than being forced by creditors or court orders.

Sole Proprietorships

A business structure where a single individual owns, manages, and is solely responsible for all aspects of the business, including liabilities.

Unlimited Liability

The potential for an owner to lose more than has been invested in a business.

Double Taxation

A situation in which the same income is taxed twice; this often occurs with corporate income taxes where earnings are taxed at the corporate level and again when distributed as dividends to shareholders.