Question

Solve this ODE Using the same approach as the solution below in Matlab Thanks: 
d4y.dt4 + 16*d3y/dt3 + 86*dy^2/dt^2 + 176*dy/dt + 105*y = 1
  using partial fraction expansion.  Note you need to calculate the roots
  of a fourth order polynomial in s.  All iniital cosnditions on y and its
  derivatives are 0
%}
clear; clc
syms Y s t
xrs = laplace(1,t,s)
eqn1 = s^4*Y+16*s^3*Y+86*s^2*Y +176*s*Y +105*Y == xrs
myanss = solve(eqn1,Y)
mypart = partfrac(myanss,'FactorMode','real')
%{
mypart =
0.020833333333333333333333333333333/(s + 3.0)
 - 0.0125/(s + 5.0)
 - 0.020833333333333333333333333333333/(s + 1.0)
 + 0.0029761904761904761904761904761905/(s + 7.0)
 + 0.0095238095238095238095238095238095/s
%}
myanst = ilaplace(myanss,s,t)
%{
myanst = exp(-3*t)/48 - exp(-t)/48 - exp(-5*t)/80 + exp(-7*t)/336 + 1/105
%}