Internal problem ID [8095]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 619.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 59
dsolve(x^2*diff(y(x),x$2)-x*(7-x^2)*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{6} {\mathrm e}^{-\frac {x^{2}}{2}}+\frac {c_{2} x^{2} {\mathrm e}^{-\frac {x^{2}}{2}} \left (\operatorname {expIntegral}_{1}\left (-\frac {x^{2}}{2}\right ) x^{4}+2 \,{\mathrm e}^{\frac {x^{2}}{2}} x^{2}+4 \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 61
DSolve[x^2*y''[x]-x*(7-x^2)*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} c_2 e^{-\frac {x^2}{2}} x^6 \operatorname {ExpIntegralEi}\left (\frac {x^2}{2}\right )-\frac {1}{8} c_2 \left (x^2+2\right ) x^2+c_1 e^{-\frac {x^2}{2}} x^6 \]