59.1.351 problem 358

Internal problem ID [9523]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 358
Date solved : Monday, January 27, 2025 at 06:03:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

\[ y = {\mathrm e}^{x} \left (c_{2} \ln \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 17

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

\[ y(x)\to e^x (c_2 \log (x)+c_1) \]