Internal problem ID [3299]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 556.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (3+6 y x +x^{2}\right ) y^{\prime }+2 x +2 y x +3 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 71
dsolve((3+6*x*y(x)+x^2)*diff(y(x),x)+2*x+2*x*y(x)+3*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-x^{2}-3+\sqrt {x^{4}-12 x^{3}-12 c_{1} x +6 x^{2}+9}}{6 x} \\ y \left (x \right ) = -\frac {x^{2}+\sqrt {x^{4}-12 x^{3}-12 c_{1} x +6 x^{2}+9}+3}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.499 (sec). Leaf size: 79
DSolve[(3+6 x y[x]+x^2)y'[x]+2 x+2 x y[x]+3 y[x]^2==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*}