Numerical solutions of differential equations

For the following questions, use Euler's method to find the approximate value of \(y\), using the given step size and initial conditions.

1. \(\frac{\mathrm{d}y}{\mathrm{d}x} = x^2 + y^2\) at \(x = 0.4\) with step size \(0.1\), given \(y(0) = 1\).
2. \(\frac{\mathrm{d}y}{\mathrm{d}x} = 2xy\) at \(x = 3\), with step size \(0.4\), given \(y(1) = 2\).
3. \(\frac{\mathrm{d}y}{\mathrm{d}x} = e^x + 2y^2\) at \(x = 0.3\), with step size \(0.1\), given \(y(0) = 1\).
4. \(\frac{\mathrm{d}y}{\mathrm{d}x} = \sin(x + y) - e^x\) at \(x = 0.5\), with step size \(0.1\), given \(y(0) = 4\).