32.7.14 problem Exercise 20.15, page 220

Internal problem ID [5929]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.15, page 220
Date solved : Monday, January 27, 2025 at 01:27:40 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{\frac {4 x}{3}}+x c_3 +c_{2} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

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

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