59.1.784 problem 806

Internal problem ID [9956]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 806
Date solved : Monday, January 27, 2025 at 06:16:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.244 (sec). Leaf size: 43

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

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