59.1.436 problem 449

Internal problem ID [9608]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 449
Date solved : Monday, January 27, 2025 at 06:04:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 23

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

\[ y(x)\to e^x \left (\frac {c_1}{x}+\frac {c_2 x}{2}\right ) \]