Internal problem ID [7000]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 269.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 34
dsolve(2*x^2*diff(y(x),x$2)-(3*x+2)*diff(y(x),x)+(2*x-1)/x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (5 x +2\right )}{\sqrt {x}}+c_{2} {\mathrm e}^{-\frac {1}{x}} \hypergeom \left (\relax [2], \left [-\frac {1}{2}\right ], \frac {1}{x}\right ) x^{2} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 60
DSolve[2*x^2*y''[x]-(3*x+2)*y'[x]+(2*x-1)/x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(5 x+2) \left (3 c_1-10 \sqrt {\pi } c_2 \operatorname {Erf}\left (\frac {1}{\sqrt {x}}\right )\right )}{15 \sqrt {x}}+\frac {2}{3} c_2 e^{-1/x} ((x-4) x-2) \\ \end{align*}