59.1.709 problem 726

Internal problem ID [9881]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 726
Date solved : Monday, January 27, 2025 at 06:15:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 94

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

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]+1}{(K[1]-2) K[1]}dK[1]-\frac {1}{2} \int _1^x-\frac {2}{(K[2]-2) K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]+1}{(K[1]-2) K[1]}dK[1]\right )dK[3]+c_1\right ) \]