Internal problem ID [8776]
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]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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)
\[ y \relax (x ) = x c_{1}+c_{2} \left (\frac {\left (x +1\right ) {\mathrm e}^{x}}{x}+x \expIntegral \left (1, -x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 34
DSolve[(-1 + x)*y[x] - (-1 + x)*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x \text {Ei}(x)}{2}+c_1 x-\frac {c_2 e^x (x+1)}{2 x} \\ \end{align*}