78.11.13 problem 10 (b, n=1)

Internal problem ID [18284]
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 16. The Use of a Known Solution to find Another. Problems at page 121
Problem number : 10 (b, n=1)
Date solved : Tuesday, January 28, 2025 at 11:45:09 AM
CAS classification : [_Laguerre]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 19

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

\[ y(x)\to c_1 e^x-c_2 (x+1) \]