59.1.668 problem 685

Internal problem ID [9840]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 685
Date solved : Monday, January 27, 2025 at 06:14:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 49

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

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