Internal problem ID [8636]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime } x^{2}+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \left (6 \,3^{\frac {2}{3}} \left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )\right ) \left (-x^{3}\right )^{\frac {1}{3}}+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 27
DSolve[x*y[x] - x^2*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {1}{3} c_2 E_{\frac {4}{3}}\left (-\frac {x^3}{3}\right ) \\ \end{align*}