Worksheet: Slope Fields and Solution Curves

In this worksheet, we will practice drawing slope fields, which help visualize the general solution of first-order differential equations graphically.

Q1:

Consider the given slope field graph. At which point is the differential equation equal to zero?

  • APoint 𝐡
  • BPoint 𝐴
  • CPoint 𝐸
  • DPoint 𝐷
  • EPoint 𝐢

Q2:

Consider the given slope field graph. Which of the following differential equations is represented on the graph?

  • A𝑦=2βˆ’π‘₯π‘₯βˆ’3
  • B𝑦=π‘₯+23βˆ’π‘₯
  • C𝑦=π‘₯+2π‘₯βˆ’3
  • D𝑦=π‘₯βˆ’2π‘₯βˆ’3
  • E𝑦=π‘₯βˆ’2π‘₯+3

Q3:

Which of the following is the slope field of the differential equation 𝑦=2π‘₯+3π‘¦βˆ’5?

  • A
  • B
  • C
  • D
  • E

Q4:

Which of the following is the slope field of the differential equation ddsinh𝑦π‘₯=π‘₯?

  • A
  • B
  • C
  • D
  • E

Q5:

Consider the given slope field graph. Which of the following differential equations is represented on the graph?

  • Add𝑦π‘₯=π‘₯+5
  • Bdd𝑦π‘₯=5βˆ’π‘₯
  • Cdd𝑦π‘₯=π‘₯βˆ’5
  • Ddd𝑦π‘₯=π‘₯+5
  • Edd𝑦π‘₯=π‘₯βˆ’5

Q6:

Consider the given slope field graph. Which of the following differential equations is represented on the graph?

  • Addsin𝑦π‘₯=π‘₯
  • Bddcos𝑦π‘₯=2π‘₯
  • Cddsin𝑦π‘₯=βˆ’2π‘₯
  • Dddsin𝑦π‘₯=2π‘₯
  • Eddcos𝑦π‘₯=βˆ’π‘₯

Q7:

Which of the following is the slope field of the differential equation 𝑦=𝑒+3οŽ˜οŠ¨ο—?

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the following is the slope field of the differential equation ddsin𝑦π‘₯=π‘₯π‘₯?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following is the slope field of the differential equation 𝑦=π‘₯?

  • A
  • B
  • C
  • D
  • E

Q10:

Consider the given slope field graph representing a differential equation. If the solution of the differential equation contains point 𝑆, which point can also belong to the solution?

  • APoint 𝐴
  • BPoint 𝐡
  • CPoint 𝐸
  • DPoint 𝐷
  • EPoint 𝐢

Q11:

The slope field of 𝑦′=𝑦+π‘₯ is shown. However, one of the quadrants is incorrect. Identify the incorrect quadrant.

  • A𝐷
  • B𝐴
  • C𝐢
  • D𝐡

Q12:

The slope field for a particular differential equation is shown. Which curve represents a specific solution to the differential equation?

  • A
  • B
  • C
  • D
  • E

Q13:

The slope field for a particular differential equation is shown. Which of the following equations could be a specific solution to that differential equation?

  • A𝑦=1π‘₯
  • B𝑦=|π‘₯|ln
  • C𝑦=π‘’οŠ±ο—
  • D𝑦=𝑒
  • E𝑦=1π‘₯

Q14:

Which of the following is a slope field of the differential equation 𝑦′=(𝑦+2)+(π‘₯βˆ’3)βˆ’25?

  • A
  • B
  • C
  • D
  • E

Q15:

The slope field of 𝑦′=π‘₯𝑦 is shown. Draw, on the same grid, the specific solution when π‘₯=1, 𝑦=Β±2.

  • A
  • B
  • C
  • D
  • E

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