Internal problem ID [7488]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 771.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.096 (sec). Leaf size: 25
dsolve(2*x*diff(y(x),x$2)-(3+2*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\relax [2], \left [\frac {7}{2}\right ], x\right ) x^{\frac {5}{2}}+c_{2} \left (-\frac {2 x}{3}+1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 48
DSolve[2*x*y''[x]-(3+2*x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (e^x (2 x-3) \left (2 c_1-\sqrt {\pi } c_2 \operatorname {Erf}\left (\sqrt {x}\right )\right )-6 c_2 \sqrt {x}\right ) \\ \end{align*}