Internal problem ID [8625]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1045.
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 y^{\prime }+\left (x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 28
dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)+(x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \erf \left (\frac {i \sqrt {2}\, x}{2}-i \sqrt {2}\right ) {\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 39
DSolve[(-1 + x)*y[x] - x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {\frac {\pi }{2}} c_2 e^{x-2} \text {Erfi}\left (\frac {x-2}{\sqrt {2}}\right )+c_1 e^x \\ \end{align*}