64.3.1 problem 1

Internal problem ID [13201]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 1
Date solved : Monday, March 31, 2025 at 07:37:17 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 49

ode:=3*x+2*y(x)+(y(x)+2*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.555 (sec). Leaf size: 79

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

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

✓ Sympy. Time used: 1.073 (sec). Leaf size: 29

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

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