show your steps please

Write a code implementing Euler's method for solving the initial value problem: C#()), 1 (0,01 TO 1. Run your code for the Dahlquist test: Xx(t). 1 (0,5) x(0) with = -1,-10, -50 and h=0.5, 0.1,0.01. 2. Run your code for cos(t)=(t), 1 (0,01 x(0) with h = 0.2,0.1,0.05, 0.025 (here the exact solution is x(t) = exp(sin(O)). For both problems: 1. Calculate the maximum error and plot the computed solution versus the true solution in all cascs. 2. Discuss the results from a point of view of stability and convergence