Internal problem ID [9389]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1056.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2} y^{\prime }+x y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )-c_{2} \left (-x^{3}\right )^{\frac {1}{3}} 3^{\frac {2}{3}} \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )+3 c_{2} {\mathrm e}^{\frac {x^{3}}{3}}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 41
DSolve[x*y[x] - x^2*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}} \]