Use Euler's method to solve for

$\frac{dy}{dx}=cosx$

in the range $0x0\mathrm{.}5$ using a step size $h$ of $0\mathrm{.}1.$ Use the initial condition $y(0)=0.$ Compare the numerical approximation against the true solution using the relative error. How does the error change as you go from $0$ to $0\mathrm{.}5?$

$2.$ Repeat problem $1$ using Heun's Method. Compare your relative errors against those you found in Problem $1.$ Which method gives better approximations?