Internal problem ID [7410]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 691.
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 (1-x \right ) y^{\prime }+\left (1-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve(x^2*diff(y(x),x$2)-x*(1-x)*diff(y(x),x)+(1-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \expIntegral \left (1, x\right ) x \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 17
DSolve[x^2*y''[x]-x*(1-x)*y'[x]+(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_2 \text {Ei}(-x)+c_1) \\ \end{align*}