Question

Use Euler's method with step size 0.2 to estimate y(2), where y(x) is the solution of the initial-value problem y' = 2 − 3xy, y(1) = 0. (Round your answer to four decimal places.)

Answer 1

Answer:

$y_2=0.512$

Step-by-step explanation:

We are given that

Step size=0.2

Initial value problem

y'=2-3xy

f(x,y)=2-3xy

y(1)=0

We have to find the value of $y_2$

Euler's method of approximation

$y_{n+1)=y_n+hf(x_n,y_n)$

We have $y_0=0,x_0=1$

Substitute the value then we get when n=1

$y_1=y_0+hf(x_0,y_0)$

$y_1=0+(0.2)(2-3(1)(0))$

$y_1=0.4$

$x_1=x_0+h=1+0.2=1.2$

$y_2=y_1+hf(x_1,y_1)$

$y_2=0.4+0.2(2-3(1.2)(0.4))$

$y_2=0.4+0.2\times 0.56$

$y_2=0.4+0.112=0.512$

$y_2=0.512$