82.48.11 problem Ex. 11

Internal problem ID [18992]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. End of chapter problems at page 107
Problem number : Ex. 11
Date solved : Tuesday, January 28, 2025 at 12:44:42 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 26

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

\[ y \left (x \right ) = c_{1} +c_{2} \left (x -1\right ) {\mathrm e}^{x}+c_3 \left (\int \left (\operatorname {Ei}_{1}\left (x \right ) x \,{\mathrm e}^{x}-1\right )d x \right ) \]

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 39

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

\[ y(x)\to -c_2 e^x (x-1) \operatorname {ExpIntegralEi}(-x)+c_1 e^x (x-1)-c_2 \log (-x)+c_3 \]