Slope fields Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following differential equations produces a slope field with horizontal line segments along the parabola $y = x^2 - 3$ and a positive slope at the point $(1, -1)$?

   • A) $\frac{dy}{dx} = x^2 - y - 3$
   • B) $\frac{dy}{dx} = y - x^2 - 3$
   • C) $\frac{dy}{dx} = y - x^2 + 3$
   • D) $\frac{dy}{dx} = x^2 + y - 3$
2. 2.

   Which of the following differential equations produces a slope field where the slopes are constant along every line of the form $x + y = c$, and line segments are horizontal precisely along the line $y = -x + 2$?

   • A) $\frac{dy}{dx} = x - y + 2$
   • B) $\frac{dy}{dx} = x + y - 2$
   • C) $\frac{dy}{dx} = x + y + 2$
   • D) $\frac{dy}{dx} = 2x + 2y - 1$
3. 3.

   Which of the following differential equations produces a slope field in which the slopes are constant along any vertical line, and horizontal segments occur precisely along the lines $x = -2$ and $x = 2$?

   • A) $\frac{dy}{dx} = y^2 - 4$
   • B) $\frac{dy}{dx} = x^2 + 4$
   • C) $\frac{dy}{dx} = x^2 - 4$
   • D) $\frac{dy}{dx} = x - 2$
4. 4.

   For which of the following differential equations does the slope field feature negative slopes in Quadrants I and III, and positive slopes in Quadrants II and IV?

   • A) $\frac{dy}{dx} = -xy$
   • B) $\frac{dy}{dx} = xy$
   • C) $\frac{dy}{dx} = \frac{x}{y}$
   • D) $\frac{dy}{dx} = x - y$