59.1.643 problem 660

Internal problem ID [9815]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 660
Date solved : Monday, January 27, 2025 at 06:14:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = {\mathrm e}^{2 x} c_{2} +2 c_{1} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 33

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

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