59.1.93 problem 95

Internal problem ID [9265]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 95
Date solved : Monday, January 27, 2025 at 06:00:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (4+x \right ) y^{\prime \prime }-x \left (1-3 x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.112 (sec). Leaf size: 27

dsolve(x^2*(4+x)*diff(y(x),x$2)-x*(1-3*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{{1}/{4}}}{\left (x +4\right )^{{9}/{4}}}+c_{2} \operatorname {hypergeom}\left (\left [1, 3\right ], \left [\frac {7}{4}\right ], -\frac {x}{4}\right ) x \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 109

DSolve[x^2*(4+x)*D[y[x],{x,2}]-x*(1-3*x)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {1-K[1]}{2 K[1]^2+8 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {3 K[2]-1}{K[2] (K[2]+4)}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {1-K[1]}{2 K[1]^2+8 K[1]}dK[1]\right )dK[3]+c_1\right ) \]