1. Solve the following differential equation by: 1) Exactly (analytically), 2) Euler's method, 3) Runge-Kutta method, and plot the three results in a single graph in GnuPlot. Use 0 ≤t≤ 1 and h = 0.1. Use the following syntax: plot "data1.txt", "data2.txt", sin(x), where "data1.txt" contains data from the Euler method and "data2.txt" contains data from the R-K method. y=y, y(0) = 1, 2. Numerically solve the following differential equations using the Euler method: du =V dt dv == -kv-u³ +B cost. dt with k=0.1, B 11.0, and plot the result using gnuplot. Change the parameters to k=0.4, B=20.0 and show the graph as well. You can use the initial condition as u(0) 1, v(0) = 1. Also, use h = 0.01, i = 10000. (1) (2)