# euler.jl -- This is Euler's method

f(t)=2*sin(t)*cos(t) 
N=20 
T=2*pi 
h=T/N 
y0=0 
y=y0 
t0=0 
ys=zeros(N)
ts=zeros(N)
for n=0:(N-1)
    global t,y,ts,ys
    t=t0+h*n
    y=y+h*f(t)
    ts[n+1]=t0+h*(n+1)
    ys[n+1]=y
end 
yexact(t)=sin(t)^2
using Plots
plot([0:0.01:T;],yexact.([0:0.01:T;]))
display(plot!(ts,ys))