Internal problem ID [9531]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1196.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+y \left (x -1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*diff(diff(y(x),x),x)-x*(x-1)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x c_{1} +c_{2} \left (\frac {\left (x +1\right ) {\mathrm e}^{x}}{x}+\operatorname {Ei}_{1}\left (-x \right ) x \right ) \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 34
DSolve[(-1 + x)*y[x] - (-1 + x)*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \left (x^2 \operatorname {ExpIntegralEi}(x)-e^x (x+1)\right )}{2 x}+c_1 x \]