85.14.9 problem 7

Internal problem ID [22525]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 41
Problem number : 7
Date solved : Thursday, October 02, 2025 at 08:46:25 PM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {1}{\arctan \left (\textit {\_a} \right )}d \textit {\_a} x +c_1 x -1\right ) x \]

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{\arctan (K[1])}dK[1]=-\frac {1}{x}+c_1,y(x)\right ] \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (y(x) + atan(y(x)/x))/x cannot be solved b