Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y2, y(0) = 3. (Round your answer to four decimal places.)

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

Putting the value of y'(x) in equation (1)

Substituting x =0 and h= 0.2

   [∵ y(0) =3 ]

Substituting x =0.2 and h= 0.2

Substituting x =0.4 and h= 0.2

Substituting x =0.6 and h= 0.2

Substituting x =0.8 and h= 0.2

Therefore the value of y(1)= 0.9152.

the answer is a beach is the best place to be