Internal problem ID [3818]
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`]]
\[ \boxed {x \left (2+y x \right ) y^{\prime }+2 y+y^{2} x=2 x^{3}+3} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {-2-\sqrt {x^{4}-2 c_{1} +6 x +4}}{x} y \left (x \right ) = \frac {-2+\sqrt {x^{4}-2 c_{1} +6 x +4}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.633 (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*}