Internal problem ID [14251]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {y-\left (x +3 y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(y(x)-(x+3*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {c_{1}}{6}-\frac {\sqrt {c_{1}^{2}+12 x}}{6} \\ y \left (x \right ) &= -\frac {c_{1}}{6}+\frac {\sqrt {c_{1}^{2}+12 x}}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 58
DSolve[y[x]-(x+3*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-\sqrt {12 x+c_1{}^2}-c_1\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {12 x+c_1{}^2}-c_1\right ) \\ y(x)\to 0 \\ \end{align*}