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=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.

Q2:

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).

Q3:

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.

Q4:

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).

Q5:

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).

Q6:

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).

Q7:

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.

Q8:

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).

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=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).

Q11:

Consider the initial value problem 𝑦′=π‘’ο—οŠ±οŠ©ο˜, 𝑦(0)=2. Use Euler’s method with 9 steps to estimate the value of 𝑦(3) to three decimal places.

Q12:

Consider the initial value problem 𝑦′=2βˆ’π‘₯𝑦, 𝑦(0)=0. Use Euler’s method with 10 steps to estimate the value of 𝑦(1) to three decimal places.

Q13:

Consider the initial value problem 𝑦′=2𝑦+5π‘₯βˆ’4, where 𝑦(0)=2. Use Euler’s method with 6 steps to estimate the value of 𝑦(3) to two decimal places.

Q14:

Consider the initial value problem 𝑦′=π‘₯βˆ’π‘¦οŠ©, where 𝑦(0)=1. Use Euler’s method with 10 steps to estimate the value of 𝑦(2) to three significant figures.

Q15:

Consider the initial value problem 𝑦′=2βˆ’5𝑦, where 𝑦(0)=βˆ’1. Use Euler’s method with 4 steps to estimate the value of 𝑦(1) to four significant figures.

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