Internal problem ID [3052]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 304.
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 }+4 y-\left (2+x \right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve((-x^2+4)*diff(y(x),x)+4*y(x) = (2+x)*y(x)^2,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: 0.218 (sec). Leaf size: 30
DSolve[(4-x^2)y'[x]+4 y[x]==(2+x)y[x]^2,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*}