Internal problem ID [4551]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.30, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\left (3+6 y x +x^{2}\right ) y^{\prime }+3 y^{2}+2 y x=-2 x} \]
✓ 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 \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: 0.477 (sec). Leaf size: 83
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 {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x} y(x)\to -\frac {x^2-\sqrt {x^4-12 x^3+6 x^2+36 c_1 x+9}+3}{6 x} \end{align*}