59.1.662 problem 679

Internal problem ID [9834]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 679
Date solved : Monday, January 27, 2025 at 06:14:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)+x*(x-3)*diff(y(x),x)+(4-x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.376 (sec). Leaf size: 60

DSolve[x^2*D[y[x],{x,2}]+x*(x-3)*D[y[x],x]+(4-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \left (c_2 \int _1^x\frac {e^{K[2]}}{K[2]}dK[2]+c_1\right ) \exp \left (\frac {1}{2} \left (-\int _1^x\left (1-\frac {3}{K[1]}\right )dK[1]-x\right )\right ) \]