74.5.22 problem 22

Internal problem ID [15986]
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
Date solved : Tuesday, January 28, 2025 at 08:25:42 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y-\left (x +3 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 37

dsolve(y(x)-(x+3*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {c_{1}}{6}-\frac {\sqrt {c_{1}^{2}+12 x}}{6} \\ y &= -\frac {c_{1}}{6}+\frac {\sqrt {c_{1}^{2}+12 x}}{6} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 58

DSolve[y[x]-(x+3*y[x]^2)*D[y[x],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*}