Internal problem ID [7245]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 525.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 29
dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \WhittakerM \left (-\frac {1}{6}, \frac {2}{3}, \frac {x}{3}\right ) {\mathrm e}^{-\frac {x}{6}}}{x^{\frac {1}{6}}}+\frac {c_{2} {\mathrm e}^{-\frac {x}{3}}}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 39
DSolve[3*x^2*y''[x]+x*(1+x)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x/3} \left (c_2-c_1 x^{4/3} E_{-\frac {1}{3}}\left (-\frac {x}{3}\right )\right )}{\sqrt [3]{x}} \\ \end{align*}