Internal problem ID [7826]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 246.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (3 y+2 x \right ) y^{\prime }+3 \left (x +y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 63
dsolve(x*(3*y(x)+2*x)*diff(y(x),x)+3*(y(x)+x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-\frac {2 c_{1} x^{2}}{3}-\frac {\sqrt {-2 x^{4} c_{1}^{2}+6}}{6}}{c_{1} x} \\ y \relax (x ) = \frac {-\frac {2 c_{1} x^{2}}{3}+\frac {\sqrt {-2 x^{4} c_{1}^{2}+6}}{6}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.495 (sec). Leaf size: 135
DSolve[x*(3*y[x]+2*x)*y'[x]+3*(y[x]+x)^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to \frac {-4 x^2+\sqrt {-2 x^4+6 e^{4 c_1}}}{6 x} \\ y(x)\to -\frac {\sqrt {2} \sqrt {-x^4}+4 x^2}{6 x} \\ y(x)\to \frac {\sqrt {2} \sqrt {-x^4}-4 x^2}{6 x} \\ \end{align*}