Internal problem ID [6740]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {5 y^{\prime \prime }-2 x y^{\prime }+10 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 31
dsolve(5*diff(y(x),x$2)-2*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\frac {4}{375} x^{5}-\frac {4}{15} x^{3}+x \right )+c_{2} \hypergeom \left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 77
DSolve[5*y''[x]-2*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {5} x \left (4 (x-5) (x+5) x^2+375\right ) \left (64 c_1-\sqrt {\pi } c_2 \text {Erfi}\left (\frac {x}{\sqrt {5}}\right )\right )+10 c_2 e^{\frac {x^2}{5}} \left (x^2-20\right ) \left (2 x^2-5\right )}{1000} \\ \end{align*}