Internal problem ID [3311]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 569.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {x \left (2-y x \right ) y^{\prime }+2 y-x y^{2} \left (y x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(x*(2-x*y(x))*diff(y(x),x)+2*y(x)-x*y(x)^2*(1+x*y(x)) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-1+\sqrt {1-4 \ln \relax (x )+4 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ y \relax (x ) = \frac {1+\sqrt {1-4 \ln \relax (x )+4 c_{1}}}{2 \left (\ln \relax (x )-c_{1}\right ) x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.715 (sec). Leaf size: 85
DSolve[x(2-x y[x])y'[x]+2 y[x]-x y[x]^2(1+x y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{x+\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x (-4 \log (x)+1+4 c_1)}} \\ y(x)\to \frac {2}{x+\left (-\frac {1}{x^3}\right )^{3/2} x^5 \sqrt {x (4 \log (x)-1-4 c_1)}} \\ y(x)\to 0 \\ \end{align*}