Internal problem ID [6917]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 185.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 45
dsolve(x^2*diff(y(x),x$2)-x*(7-x^2)*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{6} {\mathrm e}^{-\frac {x^{2}}{2}}+c_{2} x^{2} \left ({\mathrm e}^{-\frac {x^{2}}{2}} \expIntegral \left (1, -\frac {x^{2}}{2}\right ) x^{4}+2 x^{2}+4\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 51
DSolve[x^2*y''[x]-x*(7-x^2)*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} x^2 \left (e^{-\frac {x^2}{2}} x^4 \left (c_2 \operatorname {Ei}\left (\frac {x^2}{2}\right )+16 c_1\right )-2 c_2 \left (x^2+2\right )\right ) \\ \end{align*}