59.1.297 problem 300

Internal problem ID [9469]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 300
Date solved : Monday, January 27, 2025 at 06:03:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 28

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

\[ y = -\frac {\left (x +1\right ) c_{2} {\mathrm e}^{-x}}{2}+x \left (x +2\right ) \left (c_{1} +\frac {\operatorname {Ei}_{1}\left (x \right ) c_{2}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 40

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

\[ y(x)\to x (x+2) \left (c_2 \int _1^x\frac {e^{-K[1]}}{K[1]^2 (K[1]+2)^2}dK[1]+c_1\right ) \]