14.21.13 problem 13

Internal problem ID [2722]
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 : 13
Date solved : Monday, January 27, 2025 at 06:12:19 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=t +\cos \left (t \right )+2 \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

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

\[ y = \frac {\left (3+4 t -8 c_2 \right ) {\mathrm e}^{-2 t}}{16}-\frac {t^{2}}{8}+\frac {{\mathrm e}^{2 t} c_1}{2}+c_3 -\frac {\sin \left (t \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.771 (sec). Leaf size: 51

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

\[ y(t)\to \frac {1}{16} e^{-2 t} \left (-2 e^{2 t} t^2+4 t+8 c_1 e^{4 t}+3-8 c_2\right )-\frac {\sin (t)}{5}+c_3 \]