Internal problem ID [8021]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 545.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 39
dsolve(9*x^2*diff(y(x),x$2)+3*x*(3+x^2)*diff(y(x),x)-(1-5*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{-\frac {x^{2}}{6}}}{x^{\frac {1}{3}}}+\frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{6}} \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{6}}}{x^{\frac {1}{3}}}d x \right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 61
DSolve[9*x^2*y''[x]+3*x*(3+x^2)*y'[x]-(1-5*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\frac {x^2}{6}} \left (2 c_1 x^{4/3}+\sqrt [3]{6} c_2 \left (-x^2\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {x^2}{6}\right )\right )}{2 x^{5/3}} \]