Taylor's Series second order method - Matlab Code

I am wanting to compare on one plot the differential equation approximations using Taylor's, Euler's and Exact methods.

Following please find my Matlab code that still needs the Taylor's Series second order method to be included.

For the Taylor's series second order method , where the interval

I worked out by hand, and the result in Matlab for the Taylor's series second order method should be:

My Matlab Code so far (which tested fine and plots the two methods together - just need to incorporate Taylor's method now)