59.1.659 problem 676

Internal problem ID [9831]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 676
Date solved : Monday, January 27, 2025 at 06:14:49 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: 42

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

\[ y = x^{2} \left ({\mathrm e}^{x} c_{2} \left (x^{2}+4 x +2\right ) \operatorname {Ei}_{1}\left (x \right )+c_{1} \left (x^{2}+4 x +2\right ) {\mathrm e}^{x}-c_{2} \left (x +3\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.259 (sec). Leaf size: 60

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

\[ y(x)\to e^{x+2} x^2 \left (x^2+4 x+2\right ) \left (c_2 \int _1^x\frac {e^{-K[1]-1}}{K[1] \left (K[1]^2+4 K[1]+2\right )^2}dK[1]+c_1\right ) \]