For the thin, glass-walled mercury thermometer system shown in Figure 1 on the next page, assume that the temperature of the bath changes based on some chemical process in the bath. The equation that describes this process is dag) dt + 29(t) = cos 4t The response of the thermometer, 6(t), is 90:) = 0.1 c0541.\" + 0.2 sin 4: + 2.9 e-Zr The ODE given above can be solved using many numerical methods, such as Euler's and RungeKutta 2nd Order Methods. 1 . Thermometer Figure 1 Thin, giasswal'l'ed mercury thermometersystem Write an R function that computes the solution 6(t) using Euler's Method. For this step, use the following information: o h = 0.8. 0.2, or 0.05, o 60 = 3 C, . 0 s t <_: second. find the discrete values of eu at each h step value. write an r function that uses rungekutta method to solve same ode using information as in calculate relative error solution time for step. your output code should show a table shows exact temperature estimated temperature. and error. user will choose one size>