59.1.265 problem 268

Internal problem ID [9437]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 268
Date solved : Monday, January 27, 2025 at 06:02:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 35

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

\[ y = x \left (\operatorname {Ei}_{1}\left (x \right ) {\mathrm e}^{x} c_{2} x^{3}+{\mathrm e}^{x} x^{3} c_{1} -c_{2} \left (x^{2}-x +2\right )\right ) \]

✓ Solution by Mathematica

Time used: 60.067 (sec). Leaf size: 39

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

\[ y(x)\to e^{x+4} x^4 \left (\int _1^x\frac {e^{-K[1]-4} c_1}{K[1]^4}dK[1]+c_2\right ) \]