59.1.295 problem 298

Internal problem ID [9467]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 298
Date solved : Monday, January 27, 2025 at 06:03:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 45

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

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