Euler's method Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/differential-equations/euler-s-method/quiz/

1. 1

   Use Euler's method on dy/dx = x + y, y(0) = 1, step 0.1, to find y(0.3)
   1. A) y(0.3) ≈ 1
   2. B) y(0.3) ≈ 1.2
   3. C) y(0.3) ≈ 3
   4. D) y(0.3) ≈ 1.362

2. 2

   Use Euler's method on dy/dx = x, y(0) = 2, step 0.5, to find y(1)

   Answer: ____________________

3. 3

   Use Euler's method on dy/dx = −y, y(0) = 4, step 0.5, to find y(1)
   1. A) y(1) ≈ 1
   2. B) y(1) ≈ −4
   3. C) y(1) ≈ 2
   4. D) y(1) ≈ −1

4. 4

   Use Euler's method on dy/dx = y − x, y(0) = 2, step 0.1, to find y(0.3)

   Answer: ____________________

5. 5

   Use Euler's method on dy/dx = x + 2y, y(0) = 1, step 0.1, to find y(0.3)
   1. A) y(0.3) ≈ 2.5
   2. B) y(0.3) ≈ 1.76
   3. C) y(0.3) ≈ 3
   4. D) y(0.3) ≈ 2

6. 6

   Use Euler's method on dy/dx = x² + y, y(0) = 1, step 0.5, to find y(1)

   Answer: ____________________

7. 7

   Use Euler's method on dy/dx = y², y(0) = 1, step 0.1, to find y(0.3)
   1. A) y(0.3) ≈ 1
   2. B) y(0.3) ≈ 3
   3. C) y(0.3) ≈ 1.3701
   4. D) y(0.3) ≈ 1.21

8. 8

   Use Euler's method on dy/dx = x − 2y, y(1) = 0, step 0.5, to find y(3)

   Answer: ____________________

9. 9

   Use Euler's method on dy/dx = 2xy, y(0) = 1, step 0.25, to find y(1)
   1. A) y(1) ≈ 1
   2. B) y(1) ≈ 4
   3. C) y(1) ≈ 1.9337
   4. D) y(1) ≈ 0.5

10. 10

    Use Euler's method on dy/dx = 3x − y, y(0) = 2, step 0.5, to find y(2)

    Answer: ____________________