59.1.512 problem 528

Internal problem ID [9684]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 528
Date solved : Monday, January 27, 2025 at 06:13:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (x +3\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+y \left (1+x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.091 (sec). Leaf size: 36

dsolve(2*x^2*(3+x)*diff(y(x),x$2)+x*(1+5*x)*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sqrt {x}\, \operatorname {hypergeom}\left (\left [1, \frac {3}{2}\right ], \left [\frac {7}{6}\right ], -\frac {x}{3}\right )+\frac {c_{2} x^{{1}/{3}}}{\left (x +3\right ) \left (1+\frac {x}{3}\right )^{{1}/{3}}} \]

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 108

DSolve[2*x^2*(3+x)*D[y[x],{x,2}]+x*(1+5*x)*D[y[x],x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]+5}{4 K[1]^2+12 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {5 K[2]+1}{2 K[2]^2+6 K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]+5}{4 K[1]^2+12 K[1]}dK[1]\right )dK[3]+c_1\right ) \]