78.11.14 problem 10 (b, n=2)

Internal problem ID [18285]
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=2)
Date solved : Tuesday, January 28, 2025 at 11:45:10 AM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{x} c_{1} +c_{2} \left (x^{2}+2 x +2\right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 24

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

\[ y(x)\to c_1 e^x-c_2 \left (x^2+2 x+2\right ) \]