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Lesson Worksheet: Euler’s Method Mathematics • Higher Education

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

Q1:

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).

Q2:

Consider the initial value problem 𝑦=π‘’οŽ˜ο—οŠ±ο˜, 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.

Q3:

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

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

Q4:

Consider the initial value problem 𝑦=5π‘₯+2π‘¦οŽ˜οŠ¨, 𝑦(0)=2.

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

Q5:

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

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

Q6:

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

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

Q7:

Consider the initial value problem 𝑦=βˆ’2π‘¦οŽ˜, 𝑦(0)=2.

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

Q8:

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

Q9:

Consider the initial value problem 𝑦=3οŽ˜ο—, 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.

Q10:

Consider the initial value problem 𝑦=2π‘₯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).

This lesson includes 5 additional questions and 45 additional question variations for subscribers.

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