advanced euler method query

[t_n_p]

1. The problem statement, all variables and given/known data

integrate dy/dx = (1+e^y)(1+x) from x=0 using the improved euler method taking step sizes of 0.125. compare the numerical solution of y(0.5) with the exact value

3. The attempt at a solution

Firstly to find the exact value I use seperation of variables and the initial condition y(0)=0 to find that y=-ln[-1+2e^(-x)e^{-(x^2)/2}]

Subbing in x=0.5 yields 2.6518

However, using an advanced euler calculator i found online tells me this:

x_n y_n
0.00000 0.00000
0.12500 0.28560
0.25000 0.67185
0.37500 1.25597
0.50000 2.45219

That is, y(0.5)=2.45219

I was just wondering if somebody would be able to confirm this is correct.

Thanks!