Use your Improved Euler system solver to approximate the solution to Duffing's equation:

x+52x+101x3=51cos(2t) with x(0)=0, and x'(0)=0 where x is the dependent variable which is a function of the independent variable t. Use step size h=0.01. Start with initial condition x0=0 .

What are the following approximations:

x210,x215,x220,x205,x200

What I am really looking for is the initial equation for the Improved Euler System. I used x=51cos(2t)52x101x3 for my f(t,x) in the Improved Euler system. I know that the Improved Euler system looks like yn+1=yn+h(2f(xn,yn)+f(xn+1,yn+1) ) where yn+1=yn+h[f(xn,yn)] and xn+1=xn+h. I used MS Excel as my solver and I set each piece up individually and then combined them, but my approximations are not correct.