80.9.1 problem 1

Internal problem ID [18592]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 63. Problems at page 196
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:03:24 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

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

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