Internal problem ID [8158]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 683.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x \left (x^{2}+6\right ) y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(x^2*diff(y(x),x$2)+x*(6+x^2)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{2}+3\right )}{x^{2}}+\frac {c_{2} \left (x^{2}+3\right ) \left (\int \frac {{\mathrm e}^{-\frac {x^{2}}{2}}}{x^{2} \left (x^{2}+3\right )^{2}}d x \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 65
DSolve[x^2*y''[x]+x*(6+x^2)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {2 \pi } c_2 x \left (x^2+3\right ) \text {erf}\left (\frac {x}{\sqrt {2}}\right )-12 c_1 x \left (x^2+3\right )+2 c_2 e^{-\frac {x^2}{2}} \left (x^2+2\right )}{12 x^3} \]