62.22.2 problem Ex 2

Internal problem ID [12924]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:44:12 AM
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)
 

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

✓ Solution by Mathematica

Time used: 0.004 (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]
 

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