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, we have:
$$y_{1}=y_{0}+hf(t_{0},y_{0})$$
where $h=0.1$, $t_{0}=0$, $y_{0}=1$ and $f(t,y)=ty$. Thus,
$$y_{1}=1+(0.1)(0)(1)=1$$
Similarly, we can find $y_{2}$, $y_{3}$, $y_{4}$, and $y_{5}$ as follows:
$$y_{2}=1+(0.1)(0.1)(1)=1.01$$
$$y_{3}=1.01+(0.1)(0.2)(1.01)=1.0301$$
$$y_{4}=1.0301+(0.1)(0.3)(1.0301)=1.060401$$
$$y_{5}=1.060401+(0.1)(0.4)(1.060401)=1.10100501$$
Thus, the solution approximated by Euler's method at $t=0.5$ is $y_{5}=1.10100501$ which is approximately equal to $\mathbf{(C) \ 11ead0bc\_8be8\_091f\_99a0\_6bda4526a9a6\_TB6988\_11}$.

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