Internal problem ID [7403]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 684.
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 }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+x*(1-x)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (x +1\right )}{x}+\frac {c_{2} {\mathrm e}^{x}}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 23
DSolve[x^2*y''[x]+x*(1-x)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 e^x-c_1 (x+1)}{x} \\ \end{align*}