Numerical solutions of differential equations

Consider the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x} = 2x + y - 1\) with \(y(0) = 1\).

1. Using Euler's Method with increments of \(0.2\), find an approximate value for \(y\) when \(x = 1\).
2. Explain how Euler's method could be improved to provide better approximation.
3. Solve the differential equation to find an exact value for \(y\) when \(x = 1\).