65.3.21 problem 16

Internal problem ID [15658]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:22:09 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x -y}{x +3 y} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 53

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {7 x^{2} c_1^{2}+3}}{3 c_1} \\ y &= \frac {-c_1 x +\sqrt {7 x^{2} c_1^{2}+3}}{3 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.259 (sec). Leaf size: 114

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

\begin{align*} y(x)&\to \frac {1}{3} \left (-x-\sqrt {7 x^2+3 e^{2 c_1}}\right )\\ y(x)&\to \frac {1}{3} \left (-x+\sqrt {7 x^2+3 e^{2 c_1}}\right )\\ y(x)&\to \frac {1}{3} \left (-\sqrt {7} \sqrt {x^2}-x\right )\\ y(x)&\to \frac {1}{3} \left (\sqrt {7} \sqrt {x^2}-x\right ) \end{align*}

✓ Sympy. Time used: 0.756 (sec). Leaf size: 36

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

\[ \left [ y{\left (x \right )} = - \frac {x}{3} - \frac {\sqrt {C_{1} + 7 x^{2}}}{3}, \ y{\left (x \right )} = - \frac {x}{3} + \frac {\sqrt {C_{1} + 7 x^{2}}}{3}\right ] \]