80.3.18 problem 19

Internal problem ID [21182]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 3. First order nonlinear differential equations. Excercise 3.7 at page 67
Problem number : 19
Date solved : Thursday, October 02, 2025 at 07:15:58 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.071 (sec). Leaf size: 51

ode:=x+3*y(x)+(3*x+y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {-3 c_1 x -\sqrt {8 x^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {-3 c_1 x +\sqrt {8 x^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.257 (sec). Leaf size: 95

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

\begin{align*} y(x)&\to -3 x-\sqrt {8 x^2+e^{2 c_1}}\\ y(x)&\to -3 x+\sqrt {8 x^2+e^{2 c_1}}\\ y(x)&\to -2 \sqrt {2} \sqrt {x^2}-3 x\\ y(x)&\to 2 \sqrt {2} \sqrt {x^2}-3 x \end{align*}

✓ Sympy. Time used: 0.686 (sec). Leaf size: 32

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

\[ \left [ y{\left (x \right )} = - 3 x - \sqrt {C_{1} + 8 x^{2}}, \ y{\left (x \right )} = - 3 x + \sqrt {C_{1} + 8 x^{2}}\right ] \]