Internal problem ID [6820]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 89.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 y^{\prime \prime } x^{2}+x \left (3+2 x \right ) y^{\prime }-\left (1-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 27
dsolve(2*x^2*diff(y(x),x$2)+x*(3+2*x)*diff(y(x),x)-(1-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \operatorname {WhittakerM}\left (-\frac {1}{4}, \frac {3}{4}, x\right ) {\mathrm e}^{-\frac {x}{2}}}{x^{\frac {3}{4}}}+\frac {c_{2} {\mathrm e}^{-x}}{x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 33
DSolve[2*x^2*y''[x]+x*(3+2*x)*y'[x]-(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (c_2 x^{3/2} L_{-\frac {3}{2}}^{\frac {3}{2}}(x)+c_1\right )}{x} \\ \end{align*}