Internal problem ID [8701]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1121.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 26
dsolve(x*diff(diff(y(x),x),x)-(x^2-x)*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\left (\int \frac {{\mathrm e}^{\frac {1}{2} x^{2}-x}}{x^{2}}d x \right ) c_{1}+c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.23 (sec). Leaf size: 37
DSolve[(-1 + x)*y[x] - (-x + x^2)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 \int _1^x\frac {e^{\frac {1}{2} (K[1]-2) K[1]}}{K[1]^2}dK[1]+c_1\right ) \\ \end{align*}