23.1.219 problem 215

Internal problem ID [4826]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 215
Date solved : Tuesday, September 30, 2025 at 08:43:12 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x y^{\prime }&=\left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right ) \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 10

ode:=x*diff(y(x),x) = (1+y(x)^2)*(x^2+arctan(y(x))); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (x \left (x +c_1 \right )\right ) \]

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to \tan (x (x+2 c_1)) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*(y(x)**2 + 1) + y(x)**2*atan(y(x)) + atan(y(x)))/x cannot be solved by the factorable group method