74.13.34 problem 58

Internal problem ID [16400]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 58
Date solved : Tuesday, January 28, 2025 at 09:07:30 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime \prime }+16 y^{\prime }-26 y&=0 \end{align*}

Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(diff(y(t),t$3)+9*diff(y(t),t$2)+16*diff(y(t),t)-26*y(t)=0,y(t), singsol=all)
 
\[ y = \left (c_{1} {\mathrm e}^{6 t}+c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{3} \right ) {\mathrm e}^{-5 t} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[ y[t],{t,3}]+9*D[y[t],{t,2}]+16*D[y[t],t]-26*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 
\[ y(t)\to e^{-5 t} \left (c_3 e^{6 t}+c_2 \cos (t)+c_1 \sin (t)\right ) \]