87.4.14 problem 14

Internal problem ID [23280]
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 37
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:28:22 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y y^{\prime }+x&=y \end{align*}

✓ Maple. Time used: 0.150 (sec). Leaf size: 51

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

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

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 56

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

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

✓ Sympy. Time used: 1.852 (sec). Leaf size: 48

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

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