88.4.2 problem 2

Internal problem ID [23966]
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. Exercise at page 33
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:47:57 PM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y y^{\prime }+4&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

ode:=y(x)*(x^2+1)*diff(y(x),x)+4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-8 \arctan \left (x \right )+c_1} \\ y &= -\sqrt {-8 \arctan \left (x \right )+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 44

ode=y[x]*(x^2+1)*D[y[x],{x,1}]+4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {2} \sqrt {-4 \arctan (x)+c_1}\\ y(x)&\to \sqrt {2} \sqrt {-4 \arctan (x)+c_1} \end{align*}

✓ Sympy. Time used: 0.228 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 + 1)*y(x)*Derivative(y(x), x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - 8 \operatorname {atan}{\left (x \right )}}, \ y{\left (x \right )} = \sqrt {C_{1} - 8 \operatorname {atan}{\left (x \right )}}\right ] \]