Suppose $\frac { d y } { d x } = \frac { y ^ { 2 } } { x }$ , $y ( 1 ) = 2$ . Use Euler's method with step size $h = 1$ to approximate $y ( 3 )$ .
A)24
B)8
C)16
D)4
E)25
F)14
G)12
H)6

Question

Quizplus · Accepted Answer

Euler's method gives$$y_{n+1}=y_n+h f\left(x_n, y_n\right)$$$$y_1=y_0+h f(x_0, y_0)=2+1 \cdot \frac{2^2}{1}=6$$$$y_2=y_1+h f(x_1, y_1)=6+1 \cdot \frac{6^2}{2}=24$$$$y_3=y_2+h f(x_2, y_2)=24+1 \cdot \frac{24^2}{3}=24$$

Suppose dydx=y2x\frac { d y } { d x } = \frac { y ^ { 2 } } { x }dxdy​=xy2​

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