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:[tex]y_2=0.512[/tex]Step-by-step explanation: We are given that Step size=0.2Initial value problem y'=2-3xyf(x,y)=2-3xyy(1)=0We have to find the value of [tex]y_2[/tex]Euler's method of approximation [tex]y_{n+1)=y_n+hf(x_n,y_n)[/tex]We have [tex]y_0=0,x_0=1[/tex]Substitute the value then we get when n=1[tex]y_1=y_0+hf(x_0,y_0)[/tex][tex]y_1=0+(0.2)(2-3(1)(0))[/tex][tex]y_1=0.4[/tex][tex]x_1=x_0+h=1+0.2=1.2[/tex][tex]y_2=y_1+hf(x_1,y_1)[/tex][tex]y_2=0.4+0.2(2-3(1.2)(0.4))[/tex][tex]y_2=0.4+0.2\times 0.56[/tex][tex]y_2=0.4+0.112=0.512[/tex][tex]y_2=0.512[/tex]