Question

(7)-0, at the points x 71, 72, 73, 74, and 7.5 Use Euler's method with step size 0.1 to approximate the solution to the initial value pro oblemy - 2x+y The approximate solution to y'=2x-y?.y(7)=0, at the point x = 71 is (Round to five decimal places as needed.)

Answer 1

2.68

Explanation:

We are given that
`x_0=7,x_1=7.1,x_2=7.2,x_3=7.3,x_4=7.4,x_5=7.5`

h=0.1

y'=2x-y

y(7)=0,f(x,y)=2x-y

`x_0=7,y_0=0`

We have to find the approximate solution to the initial problem at x=7.1

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

Substitute the value then, we get

`y_1=0+(0.1)(2(7)-0)=0+(0.1)(14)=1.4`

`y_1=1.4`

`x_1=x_0+h=7+0.1=7.1`

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

Substitute the values then, we get

`y_2=1.4+(0.1)(2(7.1)-1.4)=1.4+(0.1)(14.2-1.4)=1.4+(0.1)(12.8)=1.4+1.28`

`y_2=1.4+1.28=2.68`

Hence, the approximation solution to the initial problem at x=7.1 is =2.68