Internal problem ID [7251]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 531.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.196 (sec). Leaf size: 25
dsolve(6*x^2*diff(y(x),x$2)+x*(10-x)*diff(y(x),x)-(2+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \WhittakerM \left (-\frac {1}{6}, \frac {2}{3}, \frac {x}{6}\right ) {\mathrm e}^{\frac {x}{12}}}{x^{\frac {5}{6}}}+\frac {c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 38
DSolve[6*x^2*y''[x]+x*(10-x)*y'[x]-(2+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \sqrt [3]{x} L_{-\frac {4}{3}}^{\frac {4}{3}}\left (\frac {x}{6}\right )+\frac {6 \sqrt [3]{6} c_1}{x} \\ \end{align*}