74.13.7 problem 24

Internal problem ID [16373]
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 : 24
Date solved : Tuesday, January 28, 2025 at 09:07:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(6*diff(y(t),t$3)-5*diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{3} {\mathrm e}^{\frac {3 t}{2}}+c_{1} {\mathrm e}^{\frac {5 t}{6}}+c_{2} \right ) {\mathrm e}^{-\frac {t}{2}} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

DSolve[6*D[ y[t],{t,3}]-5*D[y[t],{t,2}]-2*D[y[t],t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{t/3}+c_2 e^{-t/2}+c_3 e^t \]