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function y_next=Taylorstep(x,y,h,f,f_x,f_y)
% y_next=Taylorstep(x,y,h,f,f_x,f_y)
% implements second order Taylor series method for ODE
% INPUTS:
% x -- x - scalar variable
% y -- y - vector variable (a column)
% h -- stepsize
% f -- f(x,y) -- differential equation
% f_x -- partial with respect to x of f
% f_y -- derivative of f with respect to y
% OUTPUT:
% y_next -- updated value of y

y_prime=f(x,y);

y_next=y+h*y_prime+(h^2/2)*(f_x(x,y)+f_y(x,y)*y_prime);

return...
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