59.1.233 problem 236

Internal problem ID [9405]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 236
Date solved : Monday, January 27, 2025 at 06:02:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (3-2 x \right ) y^{\prime }+\left (1-2 x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x$2)+x*(3-2*x)*diff(y(x),x)+(1-2*x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 33

DSolve[x^2*D[y[x],{x,2}]+x*(3-2*x)*D[y[x],x]+(1-2*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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