59.1.63 problem 65

Internal problem ID [9235]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 65
Date solved : Monday, January 27, 2025 at 05:52:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.168 (sec). Leaf size: 28

dsolve((1+x^3)*diff(y(x),x$2)+7*x^2*diff(y(x),x)+9*x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.638 (sec). Leaf size: 39

DSolve[(1+x^3)*D[y[x],{x,2}]+7*x^2*D[y[x],x]+9*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 x-c_2 \operatorname {Hypergeometric2F1}\left (-\frac {1}{3},-\frac {1}{3},\frac {2}{3},-x^3\right )}{\left (x^3+1\right )^{4/3}} \]