Problem 1
Consider the ODE and IC: ????̈ + 2????̇ + 5???? = 0,
????(0) = 1, ????̇(0) = 0.
a) Use the trial solution method to calculate the
solution ????(????) analytically.
b) Use Matlab to plot the analytical solution ????(????)
over the interval ???? ∈ [0,6].
c) Calculate the solution numerically in Matlab and plot it in the same graph as the analytical solution. Submit the figure and your codes.
Problem 2.
Consider the ODE and IC:
????̈ + 2????̇ + 5???? = 1 + 5???? + 2????2,
????(0) = 1, ????̇(0) = 0.
a) Use the trial solution method to calculate the homogeneous solution ????H(????) , use the method of undetermined coefficients to calculate the particular solution ????P(????) , and apply the ICs to obtain the solution ????(????) analytically.
b) Use Matlab to plot the analytical solution ????(????) over the interval ???? ∈ [0,2].
c) Calculate the solution numerically in Matlab and plot it in the same graph as the analytical solution. Submit the figure and your codes.
Problem 3
Consider the ODE and IC: ????̇ + 3???? = ????−????,
????(0) = 2.
a) Use the trial solution and variation of constants
methods to determine the solution ????(????) analytically. b) Use Matlab to plot the analytical solution ????(????)
over the interval ???? ∈ [0,2].
c) Calculate the solution numerically in Matlab and plot it in the same graph as the analytical solution. Submit the figure and your codes.
