Internal problem ID [7828]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 248.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (6 y x +x^{2}+3\right ) y^{\prime }+3 y^{2}+2 y x +2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 71
dsolve((6*x*y(x)+x^2+3)*diff(y(x),x)+3*y(x)^2+2*x*y(x)+2*x=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x^{2}-3+\sqrt {x^{4}-12 x^{3}+6 x^{2}-12 c_{1} x +9}}{6 x} \\ y \relax (x ) = -\frac {x^{2}+\sqrt {x^{4}-12 x^{3}+6 x^{2}-12 c_{1} x +9}+3}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.537 (sec). Leaf size: 79
DSolve[(6*x*y[x]+x^2+3)*y'[x]+3*y[x]^2+2*x*y[x]+2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2+\sqrt {9+x (x ((x-12) x+6)+36 c_1)}+3}{6 x} \\ y(x)\to \frac {-x^2+\sqrt {9+x (x ((x-12) x+6)+36 c_1)}-3}{6 x} \\ \end{align*}