58.4.21 problem 22(a)

Internal problem ID [14591]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 22(a)
Date solved : Thursday, October 02, 2025 at 09:43:30 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {2 c_1 x -\sqrt {5 x^{2} c_1^{2}+1}}{c_1} \\ y &= \frac {2 c_1 x +\sqrt {5 x^{2} c_1^{2}+1}}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.254 (sec). Leaf size: 94

ode=(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 {5 x^2+e^{2 c_1}}\\ y(x)&\to 2 x+\sqrt {5 x^2+e^{2 c_1}}\\ y(x)&\to 2 x-\sqrt {5} \sqrt {x^2}\\ y(x)&\to \sqrt {5} \sqrt {x^2}+2 x \end{align*}

✓ Sympy. Time used: 0.719 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = 2 x - \sqrt {C_{1} + 5 x^{2}}, \ y{\left (x \right )} = 2 x + \sqrt {C_{1} + 5 x^{2}}\right ] \]