59.1.170 problem 172

Internal problem ID [9342]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 172
Date solved : Monday, January 27, 2025 at 06:01:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

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

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

✓ Solution by Mathematica

Time used: 0.265 (sec). Leaf size: 36

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

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