62.23.2 problem Ex 3

Internal problem ID [12928]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 45. Roots of auxiliary equation complex. Page 95
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:44:14 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

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

\[ y = c_{1} +c_{2} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 60.134 (sec). Leaf size: 55

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

\[ y(x)\to \int _1^xe^{\frac {K[1]}{2}} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} K[1]\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} K[1]\right )\right )dK[1]+c_3 \]