Internal problem ID [7219]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 499.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{3}+1\right ) y^{\prime \prime }+7 y^{\prime } x^{2}+9 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.484 (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)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [1, 1\right ], \left [\frac {2}{3}\right ], -x^{3}\right )+\frac {c_{2} x}{\left (x^{3}+1\right )^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.839 (sec). Leaf size: 113
DSolve[(1+x^3)*y''[x]+7*x^2*y'[x]+9*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x \left (-2 \sqrt {3} \text {ArcTan}\left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^3+1}+x}\right )-2 \log \left (\sqrt [3]{x^3+1}-x\right )+\log \left (\sqrt [3]{x^3+1} x+\left (x^3+1\right )^{2/3}+x^2\right )\right )-6 c_2 \sqrt [3]{x^3+1}+6 c_1 x}{6 \left (x^3+1\right )^{4/3}} \\ \end{align*}