87.6.11 problem 11

Internal problem ID [23328]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 53
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:37:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.155 (sec). Leaf size: 51

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

\[ y = \frac {x \left (\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (x^{2} \sec \left (\textit {\_Z} \right )^{2}\right )-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (3\right )+2 \sqrt {3}\, c_1 +6 \textit {\_Z} \right )\right )-1\right )}{2} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 55

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

\[ \text {Solve}\left [\sqrt {3} \arctan \left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )+\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.633 (sec). Leaf size: 46

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

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