88.12.13 problem 15

Internal problem ID [24069]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Miscellaneous Exercises at page 55
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:56:53 PM
CAS classification : [_exact, _rational]

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

With initial conditions

\begin{align*} y \left (1\right )&=\sqrt {3} \\ \end{align*}

✓ Maple. Time used: 0.106 (sec). Leaf size: 31

ode:=(x+x/(x^2+y(x)^2))*diff(y(x),x)+y(x)-y(x)/(x^2+y(x)^2) = 0; 
ic:=[y(1) = 3^(1/2)]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x \cot \left (\operatorname {RootOf}\left (-\tan \left (\textit {\_Z} \right ) \pi +6 \tan \left (\textit {\_Z} \right ) \sqrt {3}+6 \textit {\_Z} \tan \left (\textit {\_Z} \right )-6 x^{2}\right )\right ) \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 33

ode=(x+x/(x^2+y[x]^2))*D[y[x],x]+(y[x]-y[x]/(x^2+y[x]^2))==0; 
ic={y[1]==Sqrt[3]}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x y(x)-\arctan \left (\frac {x}{y(x)}\right )=\frac {1}{6} \left (6 \sqrt {3}-\pi \right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + x/(x**2 + y(x)**2))*Derivative(y(x), x) + y(x) - y(x)/(x**2 + y(x)**2),0) 
ics = {y(1): sqrt(3)} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out