7. Differential Equations

Approximating Solutions Using Euler’s Method — Quiz

Test your understanding of approximating solutions using euler’s method with 5 practice questions.

Practice Questions

Question 1

What is the main idea of Euler’s method for estimating a solution to a differential equation?

Question 2

If a differential equation gives $y' = f(x,y)$ and the current estimate is $(x_n,y_n)$, what formula is used to compute the next Euler approximation $y_{n+1}$ with step size $h$?

Question 3

A table of Euler approximations is generated by starting at a point and repeatedly moving by a fixed step size. What does a smaller step size usually do?

Question 4

Suppose $y' = x+y$ and an Euler estimate starts at $\left(0,1\right)$ with step size $h=0.1$. What is the first Euler approximation after one step?

Question 5

In Euler’s method, what is the role of the slope field?