49.7.7 problem 4(h)

Internal problem ID [7646]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(h)
Date solved : Monday, January 27, 2025 at 03:08:57 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

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

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