Internal problem ID [7715]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 135.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-\left (-1+x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 11
dsolve(x^2*diff(y(x),x) - (x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {1}{x}} x \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 19
DSolve[x^2*y'[x] - (x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {1}{x}} x \\ y(x)\to 0 \\ \end{align*}