40.13.1 problem 21

Internal problem ID [6755]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 21
Date solved : Monday, January 27, 2025 at 02:27:36 PM
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: 0.004 (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: 0.033 (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]
 

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