14.21.18 problem 18

Internal problem ID [2727]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 18
Date solved : Monday, January 27, 2025 at 06:12:23 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=t^{3} {\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 29

dsolve(diff(y(t),t$4)+4*diff(y(t),t$3)+6*diff(y(t),t$2)+4*diff(y(t),t)+y(t)=t^3*exp(-t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} \left (\frac {1}{840} t^{7}+c_1 +c_2 t +c_3 \,t^{2}+t^{3} c_4 \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 41

DSolve[D[y[t],{t,4}]+4*D[y[t],{t,3}]+6*D[y[t],{t,2}]+4*D[y[t],t]+y[t]==t^3*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{840} e^{-t} \left (t^7+840 c_4 t^3+840 c_3 t^2+840 c_2 t+840 c_1\right ) \]