Use Euler's method with the step size of to approximate solution to the initial-value problem at .

Question

Use Euler's method with the step size of  to approximate solution to the initial-value problem  at  .

Quizplus · Accepted Answer

Using Euler's method with a step size of 0.1, we have:

$y_1 = y_0 + hf(t_0, y_0) = -3+0.1(-3-2)=-3.5$
$y_2 = y_1 + hf(t_1, y_1) = -3.5+0.1(-2.1-2.1)=-3.92$
$y_3 = y_2 + hf(t_2, y_2) = -3.92+0.1(-1.9-2.08)=-4.138$
$y_4 = y_3 + hf(t_3, y_3) = -4.138+0.1(-1.722-2.2276)=-4.24756$

So, the approximation of $y(0.3)$ using Euler's method with a step size of 0.1 is approximately -4.24756. The closest answer choice is B.

Use Euler's Method with the Step Size of to Approximate