Suppose $\frac { d y } { d x } = 2 x$ , $y ( 0 ) = 1$ . Use Euler's method with step size $h = 2$ to approximate $y ( 4 )$ .
A)5
B)2
C)3
D)17
E)1
F)4
G)9
H)16

Question

Quizplus · Accepted Answer

Euler's method approximates the solution by iterating: $y_{n+1} = y_n + h \cdot f(x_n, y_n)$. Starting with $y(0) = 1$, $h = 2$, and $f(x, y) = 2x$, we find:  1. $y(2) = 1 + 2 \cdot 2 \cdot 0 = 1$  2. $y(4) = 1 + 2 \cdot 2 \cdot 2 = 9$

Suppose dydx=2x\frac { d y } { d x } = 2 xdxdy​=2x

Suppose $\frac { d y } { d x } = 2 x$