Internal problem ID [7496]
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]]
\[ \boxed {5 y^{\prime \prime }-2 y^{\prime } x +10 y=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = c_{1} \left (\frac {4}{375} x^{5}-\frac {4}{15} x^{3}+x \right )+c_{2} \operatorname {hypergeom}\left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 138
DSolve[5*y''[x]-2*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{200} \sqrt {\frac {\pi }{5}} c_2 \sqrt {x^2} \left (4 x^4-100 x^2+375\right ) \text {erfi}\left (\frac {\sqrt {x^2}}{\sqrt {5}}\right )+\frac {32 c_1 x^5}{25 \sqrt {5}}-\frac {32 c_1 x^3}{\sqrt {5}}-\frac {9}{20} c_2 e^{\frac {x^2}{5}} x^2+c_2 e^{\frac {x^2}{5}}+\frac {1}{50} c_2 e^{\frac {x^2}{5}} x^4+24 \sqrt {5} c_1 x \]