14.21.14 problem 14

Internal problem ID [2723]
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 : 14
Date solved : Monday, January 27, 2025 at 06:12:20 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=t +\sin \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(diff(y(t),t$4)-y(t)=t+sin(t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{-t} c_4 +\frac {\left (t +4 c_1 \right ) \cos \left (t \right )}{4}+\frac {\left (4 c_3 -1\right ) \sin \left (t \right )}{4}+c_2 \,{\mathrm e}^{t}-t \]

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 43

DSolve[D[y[t],{t,4}]-y[t]==t+Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -t+c_1 e^t+c_3 e^{-t}+\left (\frac {t}{4}+c_2\right ) \cos (t)+\left (-\frac {1}{4}+c_4\right ) \sin (t) \]