68.5.22 problem 22

Internal problem ID [17273]
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 : Thursday, October 02, 2025 at 02:00:35 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=y(x)-(x+3*y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,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*}

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 58

ode=y[x]-(x+3*y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.419 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-x - 3*y(x)**2)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{6} - \frac {\sqrt {C_{1}^{2} + 12 x}}{6}, \ y{\left (x \right )} = \frac {C_{1}}{6} + \frac {\sqrt {C_{1}^{2} + 12 x}}{6}\right ] \]