Internal problem ID [7824]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 339.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2} y^{\prime }+y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x -\frac {c_{2} 3^{\frac {1}{3}} \left (6 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) 3^{\frac {2}{3}}-6 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right ) 3^{\frac {2}{3}}+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right )}{3 \left (1+\sqrt {-3}\right )} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 41
DSolve[y''[x]-x^2*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}} \]