74.13.6 problem 23

Internal problem ID [16372]
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 : 23
Date solved : Tuesday, January 28, 2025 at 09:07:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

dsolve(3*diff(y(t),t$3)-4*diff(y(t),t$2)-5*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
 

\[ y = \left (c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{\frac {4 t}{3}}+c_{2} \right ) {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 32

DSolve[3*D[ y[t],{t,3}]-4*D[y[t],{t,2}]-5*D[y[t],t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (c_1 e^{4 t/3}+c_3 e^{3 t}+c_2\right ) \]