81.2.5 problem 3-6

Internal problem ID [21494]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 3. Exact differential equations. Page 42.
Problem number : 3-6
Date solved : Thursday, October 02, 2025 at 07:42:02 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 51

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

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

✓ Mathematica. Time used: 0.261 (sec). Leaf size: 98

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

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

✓ Sympy. Time used: 0.686 (sec). Leaf size: 29

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

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