15.1.3 problem 3

Internal problem ID [2843]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:33:52 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.272 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\tan (\arctan (x)-c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 8

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

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