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 $h=0.1$ and the following recursion: 
$$
\begin{aligned}
y_{n+1}&=y_n+hf(t_n,y_n)\
&=y_n+0.1t_n+0.2y_n\
&=(1.2)y_n+0.1t_n\
\end{aligned}
$$
Starting from $t_0=1$ and $y_0=1$, we have:
$$
\begin{aligned}
y_1 &= 1.2(1) + 0.1(1) = 1.3\
y_2 &= 1.2(1.3) + 0.1(2) = 1.56\
y_3 &= 1.2(1.56) + 0.1(3) \approx \boxed{	extbf{(B) }11ead0bc_8bea_5326_99a0_011bb7a02c15_TB6988_11}
\end{aligned}
$$

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