Worksheet: Euler’s Method

In this worksheet, we will practice using Euler's method to approximate solutions to differential equations.

Q1:

Consider the initial value problem 𝑦 = 𝑒     , 𝑦 ( 0 ) = βˆ’ 2 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find 𝑦 ( 1 ) . Round your answer to 5 decimal places.

Q2:

Consider the initial value problem 𝑦 = 5 π‘₯ + 2 𝑦   , 𝑦 ( 0 ) = 2 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find 𝑦 ( 1 ) .

Q3:

Consider the initial value problem 𝑦 = 𝑦 ( π‘₯ + 2 )  l n , 𝑦 ( 0 ) = 3 .

Use Euler’s method with 𝑛 = 5 steps in the interval [ 0 , 1 ] to find 𝑦 ( 1 ) . Round your answer to 5 decimal places.

  • A 3.95454
  • B 3.41589
  • C 5.53501
  • D 4.64696
  • E 6.67480

Q4:

Consider the initial value problem 𝑦 = 4 π‘₯ βˆ’ 3 𝑦  , 𝑦 ( 0 ) = βˆ’ 1 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find the value of 𝑦 ( 1 ) .

  • A 1.4213
  • B 0.8832
  • C 1.1533
  • D 0.3200
  • E 0.6080

Q5:

Consider the initial value problem 𝑦 = βˆ’ 2 𝑦  , 𝑦 ( 0 ) = 2 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find the value of 𝑦 ( 1 ) .

  • A 0.09331
  • B 0.05599
  • C 0.15552
  • D 0.43200
  • E 0.25920

Q6:

Consider the initial value problem 𝑦 = 3 π‘₯  , 𝑦 ( 0 ) = 1 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find 𝑦 ( 1 ) .

Q7:

Consider the initial value problem 𝑦 = 3   , 𝑦 ( 0 ) = 1 .

Use Euler’s method with 𝑛 = 5 steps in the interval [ 0 , 1 ] to find 𝑦 ( 1 ) . Round your answer to 5 decimal places.

Q8:

Consider the initial value problem 𝑦 = βˆ’ 2 π‘₯  , 𝑦 ( 0 ) = βˆ’ 1 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find 𝑦 ( 1 ) .

Q9:

Consider the initial value problem 𝑦 = 𝑦 + 1  , 𝑦 ( 0 ) = 0 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find 𝑦 ( 1 ) .

Q10:

Consider the initial value problem 𝑦 = 2 π‘₯ βˆ’ π‘₯   , 𝑦 ( 0 ) = βˆ’ 2 .

Use Euler’s method with 𝑛 = 5 steps on the interval [ 0 , 1 ] to find the value of 𝑦 ( 1 ) .

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