Approximating an IVP

Question

I wish to solve the IVP:

\begin{align} x(0) =& -1 \\ x' =& 1 + x^2 - t^3 \end{align}

With a fourth order taylor series method, I solved the ODE on the interval [0, 2] and then made the following plot:

• Is this correct? I have tried to verify with SAGE Math's ODE solver, but it couldn't compute the result. Likewise, I failed with wolfram.

Thanks for all the help!