Internal problem ID [8244]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 771.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = c_{1} \operatorname {hypergeom}\left (\left [2\right ], \left [\frac {7}{2}\right ], x\right ) x^{\frac {5}{2}}+c_{2} \left (-\frac {2 x}{3}+1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 54
DSolve[2*x*y''[x]-(3+2*x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-\sqrt {\pi } c_2 e^x (2 x-3) \text {erf}\left (\sqrt {x}\right )+2 c_1 e^x (2 x-3)-6 c_2 \sqrt {x}\right ) \]