Suppose a linear homogeneous differential equation with constant coefficients has characteristic equation (r^3-r^2-8r+12)(r^2-4r + 13)^2 = 0. Find the roots of the characteristic equation and then write down the general solution.
Solve the initial value problem using the method of undetermined coefficients.
y”+y = xe^x-cos(2x); y(0) = 1; y'(0) = 2
Find the general solution of y””’-4y”’ = 3x^2+1-e^x using the method of undetermined coefficients.
