78.9.10 problem 5 (d)

Internal problem ID [18258]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 5 (d)
Date solved : Tuesday, January 28, 2025 at 11:44:34 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 12

dsolve((x-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x +c_{2} {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 17

DSolve[(x-1)*D[y[x],{x,2}] -x*D[y[x],x]+ y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x-c_2 x \]