Internal problem ID [7895]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 415.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {5 y^{\prime \prime }-2 x y^{\prime }+10 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(5*diff(y(x),x$2)-2*x*diff(y(x),x)+10*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x^{5}-25 x^{3}+\frac {375}{4} x \right )+c_{2} \left (x^{5}-25 x^{3}+\frac {375}{4} x \right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{5}}}{\left (4 x^{4}-100 x^{2}+375\right )^{2} x^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 138
DSolve[5*y''[x]-2*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{200} \sqrt {\frac {\pi }{5}} c_2 \sqrt {x^2} \left (4 x^4-100 x^2+375\right ) \text {erfi}\left (\frac {\sqrt {x^2}}{\sqrt {5}}\right )+\frac {32 c_1 x^5}{25 \sqrt {5}}-\frac {32 c_1 x^3}{\sqrt {5}}-\frac {9}{20} c_2 e^{\frac {x^2}{5}} x^2+c_2 e^{\frac {x^2}{5}}+\frac {1}{50} c_2 e^{\frac {x^2}{5}} x^4+24 \sqrt {5} c_1 x \]