Build a fourth-degree series from a differential equation

The variables x and y are related by $dy/dx=2xy-1$ and y=1 when x=0.

Show that, at x=0, $d^3y/dx^3=-4$ and $d^4y/dx^4=12$.

Find the Maclaurin series for y up to and including the term in $x^4$, and hence find an approximation to the value of y when x=0.1, giving your answer to 5 decimal places.