74.13.27 problem 44

Internal problem ID [16393]
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 : 44
Date solved : Tuesday, January 28, 2025 at 09:07:27 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 23

dsolve([24*diff(y(t),t$3)-26*diff(y(t),t$2)+9*diff(y(t),t)-y(t)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0],y(t), singsol=all)
 

\[ y = -14 \,{\mathrm e}^{\frac {t}{2}}+54 \,{\mathrm e}^{\frac {t}{3}}-40 \,{\mathrm e}^{\frac {t}{4}} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 33

DSolve[{24*D[ y[t],{t,3}]-26*D[y[t],{t,2}]+9*D[y[t],t]-y[t]==0,{y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -40 e^{t/4}+54 e^{t/3}-14 e^{t/2} \]