Consider the Differential Equation Y' = Y - $y ^ { 2 }$

question 51

Multiple Choice

Consider the differential equation y' = y - $y ^ { 2 }$ . Which of the following statements is/are true?

• A) The function f(t) = \(\frac { 1 } { \left( 1 + e ^ { - t } \right) }\) is a solution to this differential equation with initial condition \(y ( 0 ) = \frac { 1 } { 2 }\)
• B) This differential equation has infinitely many solutions.
• C) The constant function f(t) = 1 is a solution to this differential equation.
• D) If f(t) is a solution to the differential equation satisfying the initial condition y(0) = 0, then \(f ^ { \prime } ( 0 ) = 0\)
• E) All of these statements are true.

---

Definitions:

Sherman Antitrust Act

A landmark U.S. legislation passed in 1890 that prohibits monopolistic business practices.

Federal Trade Commission Act

A United States federal law established in 1914 to prevent unfair competition and deceptive practices in the marketplace.

Price Fixing

The practice of colluding with other firms to control prices.

Marketing Channel

The paths or routes that products and services take from the time they are produced until they are purchased by consumers, including intermediaries such as distributors and retailers.