Internal problem ID [6843]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 111.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+3 x \left (x^{2}+3\right ) y^{\prime }-\left (-5 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.115 (sec). Leaf size: 35
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)
\[ y \relax (x ) = \frac {c_{1} \WhittakerM \left (\frac {1}{3}, \frac {1}{6}, \frac {x^{2}}{6}\right ) {\mathrm e}^{-\frac {x^{2}}{12}}}{x}+\frac {c_{2} {\mathrm e}^{-\frac {x^{2}}{6}}}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 47
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]
\begin{align*} y(x)\to -\frac {e^{-\frac {x^2}{6}} \left (c_2 x^{2/3} E_{\frac {2}{3}}\left (-\frac {x^2}{6}\right )-2 c_1\right )}{2 \sqrt [3]{x}} \\ \end{align*}