Internal problem ID [3310]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 568.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (y x +2\right ) y^{\prime }-3-2 x^{3}+2 y+x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve(x*(2+x*y(x))*diff(y(x),x) = 3+2*x^3-2*y(x)-x*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2-\sqrt {x^{4}+6 x -2 c_{1}+4}}{x} \\ y \relax (x ) = \frac {-2+\sqrt {x^{4}+6 x -2 c_{1}+4}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.58 (sec). Leaf size: 62
DSolve[x(2+x y[x])y'[x]==3+2 x^3-2 y[x]-x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 x+\sqrt {x^2 \left (x^4+6 x+4+c_1\right )}}{x^2} \\ y(x)\to \frac {-2 x+\sqrt {x^2 \left (x^4+6 x+4+c_1\right )}}{x^2} \\ \end{align*}