Internal problem ID [7740]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 160.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 29
dsolve((x^2-4)*diff(y(x),x) + (x+2)*y(x)^2 - 4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x -2}{\ln \left (x +2\right ) x +c_{1} x +2 \ln \left (x +2\right )+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 30
DSolve[(x^2-4)*y'[x] + (x+2)*y[x]^2 - 4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-2}{(x+2) (\log (x+2)-c_1)} \\ y(x)\to 0 \\ \end{align*}