83.30.10 problem 10

Internal problem ID [19389]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:37:08 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: 0.009 (sec). Leaf size: 27

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: 0.055 (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]
 

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