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]
\[ \boxed {2 x y^{\prime \prime }-\left (3+2 x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(2*x*diff(y(x),x$2)-(3+2*x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{x} \left (-3+2 x \right )}{2}+c_{2} {\mathrm e}^{x} \left (-3+2 x \right ) \left (\int \frac {x^{\frac {3}{2}} {\mathrm e}^{-x}}{\left (-3+2 x \right )^{2}}d x \right ) \]
✓ 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]
\[ y(x)\to \frac {1}{4} \left (-\sqrt {\pi } c_2 e^x (2 x-3) \text {erf}\left (\sqrt {x}\right )+2 c_1 e^x (2 x-3)-6 c_2 \sqrt {x}\right ) \]