Use Eulers method with step size 0.1 to estimate y(0.5),
where y(x) is the solution of the initial-value problem y ' = 3y + 3xy,
y(0) = 1. (Give the answer to four decimal places.)
Let f(x,y) = 3y + 3xy, then y' = f(x,y)
By Euler's method with step size 0.1, we have h = 0.1, then
y(0) = 1,
y(0.1) = y(0) + hf(0,y(0)) = ...
Euler's metod is employed.