Internal problem ID [3983]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise
10.16, page 90.
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 {3 \left (x +y\right )^{2}+x \left (3 y+2 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 63
dsolve((3*(y(x)+x)^2)+(x*(3*y(x)+2*x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-\frac {2 c_{1} x^{2}}{3}-\frac {\sqrt {-2 c_{1}^{2} x^{4}+6}}{6}}{c_{1} x} \\ y \relax (x ) = \frac {-\frac {2 c_{1} x^{2}}{3}+\frac {\sqrt {-2 c_{1}^{2} x^{4}+6}}{6}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.401 (sec). Leaf size: 135
DSolve[(3*(y[x]+x)^2)+(x*(3*y[x]+2*x))*y'[x]==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*}